Some advocates of integrated amplifiers would say the signal path is shorter/simpler and that the preamplifier and power amplifier sections are ideally suited to each other (And an interconnect and power cable are eliminated). There are very reasonable arguments to be made for either approach.Price is certainly an issue! And I agree that signal path is important. I make exactly the same point with our preamps- having the phono section built-in eliminates the connectivity issue that otherwise can introduce coloration.
One thing about separates is you have to pay for more chassis. The chassis and usually the power supply are the most expensive part of any preamp or amplifier so having separates and having them somehow be really inexpensive either isn't a thing, or a thing that might not be practical. We're seeing a lot of very inexpensive Chinese separates on the market right now; they look nice but unless properly vetted a lot of them have inferior parts which are problematic down the road.
If you simply don't have room or the budget integrated equipment makes a lot of sense. Like anything else (tube, solid state, class A, class D etc) execution plays a huge role.