it is not just privacy reasons, there are more to reusing the same bitcoin address more than once for receiving multiple deposits. for example the biggest problem most people will face these days is the higher fees.
Higher fees and address reuse has nothing to do with any of it,the major concern about reusing the same address is the privacy thing and even if you use multi wallet,you could still link all the other addresses in the wallet without much hurdle,so it is a big hurdle,i would rather use a mixer and usually save my coins in my hardware wallet and that the only thing i can do to secure my privacy.