It's horses for courses, a high quality cartridge on a cheap/ish arm will probably never realise its full potential, there will be limitations with the arms design, The TEAC TN300 is a great budget deck and it could possibly take a very modest upgrade cartridge but not by much
Having said that, my Audio Technica LP-5 which is fitted with a AT95EX cartridge as standard sounds great but I decided on a small up grade, so fitted a Nagaoka MP-110. The arm handled it well and my old Rega Planar 3 fitted with an Ortofon Red sounded no better, in fact it had more wow on inner tracks which the LP-5 never does. Any further mods done to my LP-5 or any budget decks will have the diminishing return on your money, in some cases quite severe, it would be better spent on a new upgrade turntable