By that I mean that they are registered and regulated within the EU and other countries they operate in. The people operating the service are known and comply with applicable regulation, so that I can be reasonably confident nothing shady is going on and that I can get legal recourse in case something is wrong.

And no, despite doing some research on Transferwise before using them I didn't run into horror stories of them freezing wires. Transferwise has always been very professional and helpful in interactions with me (more so than my own bank).

Have you ever transferred 120,000 EUR with them, or - you know - any serious amount?

My transfers were in the 1k-10k range, I guess that's not "serious" for you.

But no, if I were putting such a big amount of money in their hands at once I would certainly do more research and look for better safeguarding.

Its not a matter if its serious to me. If i see quarter on the street I pick it up because money is money.

Unfortunately all those money-wire services are registered in UK and UK has the most strict KYC rules I think ever existed in free commerce. If you start sending bigger amounts they will shut you down, no matter how much due diligence you provide they just scared of repercussions, just in case.