Many nozzles can actually be beneficial (engine-out capability) or neutral (Soyuz rocket family flies for 60+ years with 32 nozzles running at the start).

According to Chertok, problems were with engines quality themselves (e.g. insufficient manufacturer experience), CORD system (new electronic system to manage many engines), absence of test stands for integrated first stage (given single-start engines, could be insufficient). Number itself isn't a problem, as demonstrated by e.g. Falcon Heavy - it's the novel N-1 rocket, which both failed and had many engines, which leads to conclusion these are related a certain way.