Those you see every day who buys and sells are mostly traders while institutions are known as a long term investor. They can sell after some time but I think it does not automatically mean that the price of Bitcoin will now fell down as not all institutions or retail investors are doing the same thing. Others are only continuously buying more coins.
On the other hand, the value of the painting are not only based on how old or new it is but it's also based on its quality. I don't only get on how we ended up connecting it from Bitcoin. I think there are other things which are more comparable to Bitcoin. You already mentioned one of it in fact. That is fiat money.
Most cryptocurrency exchanges charge a fee based on what the client receives. That means, on the BTC/USD market, the exchange takes a fee in BTC when the client buys and in USD when the client sells. Assume the average fee is 0.1%, so it can be concluded that most exchanges also might accumulate Bitcoin (is they don't sell fees in BTC).
