does low cut off in jee mains increases my chances of getting good NITs or good trades than what I'd have got had the cutoff been more?

No, low cutoff does not mean that you've got a chance of obtaining a better NIT. Solely because of he fact that the seats in NITs will still be filled according to the ranks, i.e. from top rank to a lower rank. Thus the top rankers will occupy seats first and then the subsequent rank holders.

You need to understand that cutoff has gone low only to qualify the requisite number of candidates for JEE Advanced which is 2.2 lakh. Otherwise, all of the things remain the same as it used to happen previously. Hope you're getting my point.