I get that people hate MR X and Nemmy being around, but when you look at it lore wise, they exist because of their mission parameters.
T-103 was sent in to retrieve a sample of the G virus, as well as eliminating anyone in it's path. 4 others were also dropped within the city, mostly to hold back the US military at the dead factory (which again makes sense as to why they'd pursue their targets).
Nemesis is a more advanced and the last line of T-103 models. It was designed to take orders, no matter what form it would take, as well as carrying them out with whatever weapons it was given. It's sole mission was to eliminate STARS members, and in the OG game, it killed one, but failed to kill the other (Jill). It makes perfect sense for Nemmy to track you down, just like it did in the old game.
What annoys me about the new Nemmy, is how it's been given more fluidity to it's movements, as well as being given far more moves to make use of, which makes dealing with it a practical impossibility, but at the same time it isn't, thanks to cutscenes and deus ex machina moments, which in the end make his entire new design a bigger flaw than the original, because with the original, you just filled it full of lead until it dropped. After you leave that area, Nemmy would get back up and jog off somewhere else, either for new weapons or to recuperate.
I prefer the old nemmy, because most of the areas you fought him in where transitional areas (like going into the RPD, the dead factory, the clock tower etc, all areas you hadn't visited just yet or were going to for the first time), while the new game mostly has you running back and forth within the same areas, then having him show up and chase you around, until you're basically forced down the linear path this new Remake has set out for you (which also annoys me).
T-103 in REmake 2 was better imo, because he would actively walk throughout most areas of the RPD, trying to find you, but not knowing exactly where you are. To me that felt great, because it not only gave me the chills, but I didn't feel like I was being forced to be on the run all the time, not like with new Nemmy, who always makes me wanna run for the hills and never bother with him, because the game keeps telling me "no, only through scripted finisher scenes".
I feel like Capcom blew a load of wasted potential with new Nemmy. Locking him to certain scenes, making him practically invincible in others, just ruins the immersion and believability for me, that he is someone I can defeat.