Rated thrust for most turbojet/turbofan engines means flat-rated thrust - holding a constant thrust over a wide range of OAT. Over this temperature range, the air density varies quite a bit, so the rotor speed required also varies, holding the same rated thrust. Higher OAT, lower density, higher N1 for the fan. Holding a constant thrust means the static structures (bearing housings, engine mounts, pressure vessels etc.) have stable design criteria.
This all works great up to the flat-rate (or corner point) OAT. Beyond this point, we start worrying about temperature levels, so thrust (and N1) start reducing to keep from cooking the turbine. So the max N1 occurs at the flat-rate temperature - typically ISA+15 (i.e. 30C at sea level).
But as mentioned earlier, the displayed N1 percentage is purely an arbitrary number. Every engine model has 100% defined differently. BTW, I've never heard of bearing speed being a speed limitation, and I've been in the game over 45 years. The limiting speed is always determined by stress loads on the blades and rotor discs.