The latch pin just prevents the output of the shift register going to the outputs, it does not prevent the shift register from working inside. So you can not disable shift registers like you think you can.
If I split them into groups like mentioned before would that not fix that issue of signal degradation since it will only be going through 10 shift registers at a time right?
No it wouldn’t. Signal going through a shift register is reconstituted at each stage it is not degraded at all. What degrades a signal is being connected to lots of inputs like the clock signal, that is cured by buffering in groups of ten or so.
That means the Arduino output goes to say the input of five buffers. Then each buffer output can connect to ten other inputs.