The reason they do this is because otherwise they block the requests.

I'm not sure what the issue is with publishing your email address in principle, you are reaching out, you want to inquire about some business. If anything use a different address. But why would you asymmetrically expect businesses with websites to bend over to give you all the advantages, they need some assurances as well.

Anonimity usually works one way, one party can be anonymous, not both, if you come from consumer land, it's the companies exposing themselves and doing all the compliance, if you choose privacy and force the companies to expose themselves, you'll get your wish granted, but there will be a cost, it's unlikely you'll be in the more advantageous position.