How does spending Bitcoin alert anyone to how big a stack is?
You don't alert HOW MUCH you have, but the act of HAVING bitcoin.
Currently, few people own bitcoin. It being an asset that cannot be censored or stopped makes it an excellent asset that can be forcibly expropriated from a person and passed to the bad guys without you being able to do anything.
In the future, when more people have it, and the fact that you are a bitcoiner does not raise suspicions, that is, being a bitcoiner is commonplace, this will not be a problem and consequently there will be no problem for people to use it more for everyday purchases.