Developing new engines takes time, and time was a precious resource in the Moon race.
The major problem with making larger engines is the problem of combustion instability of large combustion chambers. This is a problem that gets dramatically worse as you scale up engines. It's not an unsolvable problem, it just takes careful injector design, focused R&D, and at the time completely new technology leaping into the unknown.
Progress on rocket engine technology was made extremely quickly back then. The actual engine used, the NK-15 is also an example of that. Just as the F-1 solved the problem of combustion instability in large chambers, the NK-15 solved the problem of oxygen rich staged combustion, making it an extremely performant kerosene/LOX engine still an attractive option up the the current day.
So what to do when under extreme time pressure?
- Option 1: Hope the issue of combustion instability can be quickly solved, develop a new cutting edge engine in record time. (Probable result: rushed engine technology having a high chance of launch failure)
- Option 2: Use an existing high performance engine, and hope that the complexity and integration problems of running many in parallel can be solved in a short time (Probable result: rushed integration having a high chance of launch failure)
Using components that actually exist seems like a reasonable decision with some chance of success. But the time crunch was going to cause problems anyway.