As an American, I'd love to hear from our EU folks how they travel within the EU. Especially, in the core "countries" like a French person popping over into Germany or Belgium. Or a Spaniard popping over to Portugal or France. Or an Italian heading around the coast to France or Spain. Day trips, holiday weekends, or get-aways by car across the many unsecured borders.
This thread is so nostalgic for me, as it's such a perpetual discussion on here. My take was and is still at odds with many here, but as an American who lived in Europe over over a decade, we only tried money belts precisely once, my husband hated it, it was hot, and he refused to use it again and I certainly wasn't going to. We also don't bother with hotel safes. We leave our passport in a specific small compartment in one of our bags in our rooms when traveling. We did always travel with them, of course, even though we weren't always asked to show them, even when flying (our military ID cards were often sufficient and more easily replaceable).
Ironically, the one time after the moneybelt incident, based on the advice from this forum, I did decide to keep our passports on my person, in cross-body messenger bag with a narrow compartment that fit them well. And that was the one time our passports were presumably stolen - I never saw them again. I did not notice them being stolen, which seems impossible, but they were gone. After that, I always left them in a bag in our hotel room. I really think cases of hotel room thievery are far more unlikely than people think. It's a possibility, yes but all travel comes with risks, and this seems like the smaller one to me.
One thing I used to say on here was that as an American living abroad, I was subject to the same concept that I always had to have proof on me that I was legal to be in the country, but in 13 years, including traveling very frequently, the only time I was asked for a passport was at the airport or one very rarely on a train at a border crossing.
I personally think it's riskier to have it on your person unless it's in a hidden money belt or neck wallet, and I refuse to travel with those. I have multiple methods of payment in multiple places. Even if someone stole my purse, I'd have another card back at my hotel to pay with, etc.
If you're willing to wear a bit of underclothing to secure your passport, that is safe and I understand why even though I find it unnecessary. I would not travel with my passport and all my cards in any sort of bag, that's much more likely the way things get stolen as opposed to leaving it secure in your hotel with our without a safe (again, never used those).