Is it only writing that the cache effects and not the reading?
Theoretically, that should be the case. NAND as a media is quite slow. The problem is because it requires a bit to be erased, before it can be rewritten. It is further compounded by the fact its organized into blocks, which are basically many bits being triggered at once. SLC isn't too picky, but once you go MLC, it gets a lot worse.
Modern SSD controllers use sophisticated algorithms and big DRAM and SLC buffers to mitigate that. Also in most cases, you aren't stressing the I/O for a sustained period of time, so there are significant periods where the controller does its stuff to further reduce lags due to write-erase-write.
At 600MB/s, you are still largely under the effects of the controller and the caches. If it truly exposed the NAND media, you'd be crawling at <1MB/s sec. It could also be that the files you are writing is mostly large files that aren't totally random.
Reads shouldn't affect the drive. Well, maybe if you do a large amount of write and then read a large amount, the whole thing might slow down. That's not what you are asking though.