I have never had any kind of trouble while withdrawing satoshis from Stake, I would say it is straightforward and they explicitly say how much they would discount in order to cover the mining fees.
In my experience, the withdrawals take some minutes, which it is acceptable when we talk about Bitcoin, at least the staff knows how to balance the fee good enough so the transaction can be mined as soon as possible, without overpaying.
My first impression is that Stake's fee calculator is better than most of non-custodial wallets I have tried have.
That's what you get when you have been in this business for 10+ years or so. They had to deal with larger than normal size fees whenever they wanted to help us with our withdrawals, so they had to handle all the things that they are doing. At this point I wouldn't be shocked if they were really building their miner base neither, because they are literally that large and could do it if they wanted to, or just pay someone to do it for them.
All in all, I believe that they are too big to not realize that fee structure is an important thing, and the lower they can make it, the more customers they would get and been around long enough to test many things until they found the cheapest.