As discussed in this other thread, the biggest problem with having lots of little engines is that lots of little engines means lots of small fuel and oxidiser lines (whereas, if you use a few big engines, you can get away with using a few big fuel and oxidiser lines). Which, in turn, creates two problems:
- More complicated plumbing makes it a lot harder to ensure that the fuel and oxidiser flow is stable and uniform - especially when you have a lot more engines that all need to be producing the same amount of thrust. As a result, designs with huge numbers of engines often have severe problems with fuel- and oxidiser-flow instability, which leads to combustion instability, which causes the chamber pressure of the engine suffering from it to fluctuate, which affects the amount of fuel and oxidiser that enters the engine, which worsens the instability, all of which induces vibrations (called "pogo oscillation") in the vehicle structure, leading us to the second big issue:
- Having lots of small propellant lines makes the rocket's plumbing much more fragile - smaller, thinner lines break more easily than bigger ones, and there're more lines that can break. When you have a vehicle that's already prone to severe pogo oscillation, fragile plumbing is not your best friend.
Look at the Soviet N1 rocket for an example of the problems that can arise when using lots of little engines. Of the four N1 launch failures (which comprised the N1's entire operational history), three occurred after parts of the rat's nest of plumbing feeding the 30(!) engines in the N1's first stage ruptured for one reason or another (pogo oscillation in the first launch, an exploding turbopump in the second, the fuel/oxidiser equivalent of a water hammer in the fourth), setting parts of the stage on fire, which rapidly burnt through various important components.
TL;DR: Having lots of small engines means having lots of complicated, fragile plumbing, which is generally ungood for a rocket.