I'd never fit different profile sized tyres period
As it is, i dont even fit different axle set tyres either, even if they are matching pairs, i'd rather have safe predictable handling.
Imagine your'e going along motorway & suddenly there's something in your lane (e.g. a concrete block, as my mate found to his cost when he was on a scooter

) & you had to swerve violently to avoid the object. You will inevitably cause the car the car to slide, i'd rather have 4 wheel's sliding predictably which would give me a fighting chance to sort out regardless of whether the car has switched from understeer to oversteer & vice versa a few times as the car will bound to be fishtailing when doing 70mph.
Imagine mismatched tyres, even axle sets, what happens??? One set of tyres will have either less or more grip, it just means you've got a level of unpredictability which gives you less of a chance to sort out, could be the difference between having an accident & not.
For the sake of a few quid, i always have 4 matching tyres, i also regularly change the fronts to the rears to ensure that at least they are wearing at a similar rate. Bad enough in the dry, but in the wet it could cost you your life & any passengers with you.
It's bad enough not having any ABS in my txd, thats why i dont take the risk. Perhaps with abs equipped cars, the difference isnt quite so pronounced, but i still wouldnt take the risk as all the cars i've owned with or without abs, asr etc...have all had 4 matching tyres. Yes there's been a few times when i've had only matching axle sets, not my choice, but i've soon changed over as soon as funds have allowed & i've taken care in the wet as the handling has been on occassion, hopeless
I know some of the responses may say "I've been driving 30+ years & never had a problem", my response would be "Yet", it only takes one incident & thats that. Oh, i also regularly check my tyre pressures, at least every 2wks & always if i'm going on a longish journey.
One of the issues i've found with trying to keep 4 matching tyres, is that the tyre manufacturers have a very annoying habit of changing tyre models every couple of years or sooner, so it can be difficult to find a couple of tyres to match the other part worn already on the car, luckily the internet has managed to solve that issue for me.