The Last UK's piano factory

Nice video. They seem down to earth. Good luck to them.

Five month build time. Evidently output of about one piano per week, which sounds like quite a lot when you're such a tiny concern.

A few other videos on the website. Jamie Cullum seems suitably impressed.
https://youtu.be/KaLzFa1THYs

http://www.cavendishpianos.com/
Looking at their links section it sounds like they are yet another piano maker using the Renner actions.

I can speak to some of that, at least to a small degree.  Yes, they do need very special care and to have been fortunate in the humidity, temperature, and lack of sunlight.  When you compare the number of violins that survive from the 19th century and earlier, an amazingly high number remain in playable condition--say 1 in 10 to 1 in 100, but less than 1 in 10K to 1 in 100K pianos remain in playable condition (the statistics may be even worse--when I have the time I need to look in Ehrlich's "The Piano: A History" or "The Cambridge Companion to the Piano" to get exact numbers on how many pianos were made before 1880 which if memory serves is listed in both places--Dolge's "Pianos and their Makers" may also have it which could in the public domain and online if someone wants to be beat me to it).

Pianos are much, much larger than a violin; a violin basically only needs a soundboard (front piece), a backplate, ribbing or a rim with lining to hold those together with glued corner blocks, a neck, a scroll, a bridge, a tailpiece, an endpin, a fingerboard, and four low-tension strings to be a violin.  I do not in any way want to diminish the extremely careful craftsmanship and design that goes into those handful of parts, but there are so few parts, and all of those pieces can be replaced/repaired in some way except the front and back pieces.

A good luthier can totally disassemble a violin and reassemble it in a few hours to make--sometimes drastic--repairs: if you totally disassemble a piano, you'll have probably destroyed the soundboard (which is like destroying the front piece or back piece of a violin) and you'll definitely need to restring the entire instrument with new strings--a simple problem for a violin but an extreme project for a piano technician or rebuilder.  Piano actions, even following the simplest Cristofori or--later--Erard designs contain many hundreds or thousands of parts, and contemporary actions come to totals (depending on how specifically you want to count something as a part) in between 6K and 9K parts in the action alone (though arguments could be made that actions have only 2K to 3K parts but either way it's still a frighteningly big number).  Keeping all of those parts in working condition is horrendously expensive and replacing an entire action and getting it newly integrated into a piano usually costs enough to make replacing the piano a more viable financial option.  The problems only increase exponentially with time, as wood does not age well for mechanical stability, though it does age well for tone and resonance.  Perhaps if more metal had been used in early piano design (and perhaps in modern piano design--though ABS plastics and carbon fibre are taking over more and more as they're light like wood and hold their shape like metal--and maybe more engineered wood that doesn't expand and contract that's starting to be very popular in home building will find its way into pianos), there'd be more surviving specimens...

Pianos prior to the 20th were made very poorly and expediently (and were priced accordingly) and depended on wood to support the passive mechanical stress of the string tension and the active stress of hitting hammers against the strings.  Liszt would famously wear out multiple pianos during every single recital, so during intermissions a new piano would be brought onto the stage.  A violinist can put immense strain on the strings during a virtuostic performance to be sure, but that will (barring a grand emergency) only break a string or release the bow hair (and they immediately swap with the Concertmaster anyway): not something that requires a new scroll and neck to be carved, whereas when a piano's pinblock stops holding tune, you will have to disassemble most of the piano, mill an entirely new pin block  (out of very specialized plywood--I'm still groaning over the Youtuber who made one out of Oriented Strand Board) and put in all-new strings.  Yet another high-cost project that could be worth more than the piano is.

Some early pianos had cast iron support frameworks but not solid-cast harps like we have now, even in the lowest-end pianos.  Without the strength of a cast iron harp, the bridges and pin block will wear out quickly and need total replacement, which--often if the bridge is damaged--means replacing the soundboard too, and by that point almost none of the original piano is left.  The normal total lifespan of a 19th century piano was 5 years--only with turn-of-the-century design innovations and manufacturing changes did pianos move to the 80-120 year lifespan we're used to now.

Keeping a violin in playable condition is much simpler based on its small size and (compared to a piano) lack of wood to age.  The (comparatively little) wood that violins do have essentially petrifies with time which brightens the tone and helps the sound project, which is much of what the video is talking about when making them more desirable with time.  A Stradivarius of today sounds quite differently from one in his time, because the violin necks were extended in the nineteenth century (to fit their musical tastes) and the wood has aged, and a Stradivarius of the 2100s or 2200s will also sound materially different (if the petrification process hasn't turned them all to dust by then).  That's the reason that the "Messiah" Stradivarius in the Ashmolean Collection at Oxford University is considered especially one-of-a-kind, they are working to preserve it in exactly the condition it is now, so that future decades/centuries can directly compare it to our contemporary notion of the sound of a "perfect" condition Stradivarius.

Obviously I'm leaving out several books worth of good information, especially surrounding how much a piano actually can be rebuilt or what kinds of damage make violin repair impossible, but overall, the size and way pianos wear down with playing (violins remain in better condition as they're played regularly--a violin kept in an attic, even one with good humidity and temperature, will always be in poorer condition than one that is used consistently) means that they will always have a shorter lifespan and require much greater maintenance.

As far as rebuilding changing the value/authenticity of a pre-modern piano, that's hotly debated, but there is no question that the sound is never exactly what it was at the time whether the instrument is rebuilt or not--fresh wood and centuries old wood are physically different in a way the changes the sound.  Antique instruments of any kind need special care and also are tuned and maintained differently and by technicians who specialize in period instruments.  While this only my opinion, I'd say that when a technician rebuilds something well, it's as authentic as possible and therefore can be considered appropriately or practically authentic.  I also find that newly built instruments designed to replicate antique instruments do extremely well at being authentic: yes, again, it will never be exact at replicating the past, but it is a fine, high-quality surrogate.  But, I also grant that putting on a gray wig and wearing a badly tailored 18th-century jacket will not make someone's Bach harpsichord recital any more genuinely Baroque.

Maybe harpsichords  - which are a bit like large guitars anyway - keep better.  My own experience, having owned a Rubio copy of the 1769 Taskin for many years, was amazement at playing the original in Edinburgh.  (I was very fortunate in that it was freshly prepped for a recital later that day) Granted I didn't play them side by side, so I'm sure there were differences, but they were not obvious.  Quite a weird experience and one I shall never forget.

Huh?
It sounds like you are actually implying that the tension on the strings is some measure of inherent comparative musical goodness!