You'll find that if you don't hire a safe (where the service is available) then your insurance policy will/can become void, as the insurance "people" will interpret this, as you not having taken all reasonable measures to safeguard your valuables.
I guess thieves are less likely to walk off with a suitcase, but who knows!.
Oh don't you believe that,

people walking in/out of an hotel with a suitcase are not going to attract anybodies attention, and don't you think that the thieves know that too.?
One hotel that I stay in had a spate of burglaries a few years ago, they took the safe !
The safe was bolted to a wooden shelf in the wardrobe, so they just knocked out the shelf, broke the wood away from the safe and put the safe in an holdall and casually walked passed the reception and out of the hotel.
Another thing, the hotel itself will insure their safes and you have a case to address the hotel, if anything is take from it.
It baffles me when people spend thousands of pounds on a holiday, clothes and whatever, then skimp on the cost of a safe, which is around £1.50 a day.

but of course it's never going to happen to them, is it.?
Sorry, but I think some people just need to get their priorities right and I have no sympathy for anyone who doesn't hire a safe.
Yes, it seems like an added expense that we could all do without, it's money we could all spend on other things, but the number of times people come on this forum bleating about how they had their passport nicked/lost because they walked around with it every day, instead of taking advice from the TO's, the Passport Agency and the Home Office to keep it in the safe, or when jewellery from their room goes missing because they left it in full view for temptation.
They waste the best part of their holiday getting the crime reported and arranging another passport to fly home, plus the emotional upset. If I couldn't afford a safe, then I can't afford to go on holiday.
IMO: It's just not worth the hassle and if I've put everything that I value in a safe, then I've done everything that anyone could ask of me to safeguard my valuables.
Sanjiiiiiiiiiiiiiiiii