With regards to the frequency of an EICR in rental properties I know that most if not all large social landlords, housing associations, councils, etc do an EICR at every change of tenancy. I used to do EICR's for a chap I knew who rented a number of properties and I used to do his at every change of tenant, and a lot of the time it was a good job I did.
The only one I never charged him for, and it was one of those loss leaders, I suppose you'd call it was when I'd inspected a property and the new tenant moced in, only to move out again a month later.
I know landlords may not like paying for what they see as unneccesary paperwork (having these tests done) but they have no idea of knowing the installation is safe when the previous tenant moves out, can they be sure they haven't messed with the wiring? no they can't, The chap I used to work for ended up putting something in his tenancy agreement that only his electrician (me) was allowed to do any work on the properties, recently another friend of mine began to rent out a property, I did the EICR on it and after a year the tenant moved out, I went back and retested, everything was in good order, the tenant hadn't messed with anything. However after they advertised it again a prospective tenant came to view the property and loved it, they did however have one request, if they rented it they'd like to replace the existing light fittings with their own, would this be possible?
My mate didn't really want to do this, but said it could be done at their expense, provided it was me who carried out the work, they declined this, they were more than capable of swapping a few light fittings! Needless to say they didn't end up renting the property, he didn't want them messing about with the wiring and I don't blame him, back in the day before Covid closed all the pubs it was amazing how many plumbers, electricians, joiners, etc could be found in even the smallest pub on an evening, or at least that's what they said they were, lol
The bottom line is it's up to the landlord to be able to prove that the gas and electrical systems in their rental properties are maintained to a safe standard, and I think if someone was to move into a rental and then get hurt as a result of something the previous tenant had done the landlord would be on a very sticky wicket indeed.