My personal experience was with SWDA, it spots $11B AUM, but traded rather thinly for that figure, e.g. today only ~35 trades, and there’s a good amount of spread last time I tried to sell it
Now I’m only going for the biggest and most liquid funds. VTI is traded much much more heavily.
I don’t think it’s specific to american brokers. Buy some AAPL at a swiss broker and I’m pretty sure it’s going to be your swiss broker’s name too on the books of Depository Trust Company - the central US stock depository. It’s just how today’s electronic trading works. It’s probably similar in some other countries, but these things are not really my area of expertise.
In US at least an alternative you can elect for is “Direct Registration System”, where your stock ownership is recorded directly with the stock’s issuer. If issuer goes belly up, the chances are his stock’s most likely a zero too, so there should be little extra risk here. But trading is a hassle, whenever you want to trade you’ll need to transfer shares back to the broker.
We discussed the issue of estate tax already in another thread: The $60'000 cap for US investments