Game devs are funny. As soon as they have to taste their own medicine all hell breaks loose.

Most games are restricted in terms of how many installations are possible. It is impossible to sell games bought in a digital store anyway.

Where is the problem with paying a fee for every installation? Your games success builds on that engine. The game studio profits from each and every sale. You're free to use another engine if you don't like their business model.

But don't fret. I'd have some other suggestions, which definitely make both sides happy. They've been proven time and time again by successful games, so I doubt game developers are against it.
Provide an unfinished engine. Fix only what is necessary. Then let game studios pay for each module they want to use. Call it DLC. It's an easy way to allow game studios to only pay for the experiences they like.
It is necessary to prevent usage of unwanted extensions. Game development is an art, and no one should cheat by using, for example, third party AI to create code or art. Have them install surveillance software, able to control their whole system. Call it anti-cheat. It doesn't matter if they work alone, only with their own team, or don't use extensions on their own volition. Every developer can be a cheater. Mass surveillance software is necessary to keep the game dev community safe.
Gather system information to improve the engine. You won't use it for any other purposes anyway. Who cares if somebody may know how many systems you use, what hard- and software runs on it, and so on? Nobody would get the idea to gain any information about a studio's size, or money they put into development from that data. No one gains an advantage knowing which software they use. Marketing will never use user profiles generated from all that data.
Force access to their documents folder for no reason whatsoever. As with an anti-cheat, no one is interested in "grandma's secret recipe" (or private pictures taken, medical documents, code, theses, ...) anyway. Access simply is necessary to save game development data. There definitely isn't the possibility to use any other directory for that purpose.
Last but not least: Don't allow engine usage without their full agreement to all these terms and conditions. They may think it exceeds what would be necessary to use the engine. But if they don't like it, it's their fault for not seeing the bigger picture.