Well you can theroetically run older apps in System 7 (I know there were cutoffs like today.) Very likely in 7.0/7.1. The Mac Plus had a very long shelflife between the manufacturing and the app support, because that model like you had mentioned was the "minimum" Mac.
I have a Color Classic, 9" incher - difference is other than color, I can add more RAM beyond the 4MB hardwired memory, unlike the Plus where 4MB was the maximum. It can handle System 7.5.x fine, but I get no memory errors on occasion, partially because I have too much unneeded apps for an antique machine.
System 7 had more multitasking abilities compare to prior versions, which explains the reason why it would've been a memory hog, and why the Macintosh Plus can't run it well. Not sure about Classic Mac OS, but maybe processes might had went up in power for system resources, but I don't know that for sure.
I'd really love to see if any Mac Plus could run something "modern" (because the "Mac OS" brand has been around for more than a decade and is in many people lexicons.) Mind you, of course, that appeared in the startup screen of course! Actually, 7.5.3 was the first OS with the modern brand.