I think it's wise to assume there are lots of things you aren't doing that the same high level cubers are, outside of mechanics. For example, choosing A pair rather than B or C pair based on reasoning beyond what immediately seems the most efficient, or linking two muscle-memo'd 2gen sequences and finding shortcuts in execution at 9tps while focusing on LL EO. All the moves are easily explainable to most cubers, it's just speed and creativity of application that sets them apart. 'Knowing the path' isn't the same as sprinting down it full pelt! So with your practised solve, yeah, not only is there a significant difference in sustained tps (having fingertricks for a large variety of move sequences), but also a significant difference in pair selection and general solve ergonomics.
Anyway, tps on its own is unimportant for the most part. Sustaining an efficient 4tps is much better than inefficient bursts averaging 4tps in many, many ways. Like you've said I'd focus on smoother solves, and being confident in your intuition is usually the main thing I see your level having problems with (constant double-checking of knowledge you already have), along with a focus on pieces you know you're just about to solve anyway.
Regarding 'slow solves', I'm perfectly comfortable turning in a way I perceive to be slow and getting 11-12 second solves, even though the actual tps is relatively high, simply due to each move being done efficiently in consideration to neighbouring moves, and I think this is a big element that's hard to translate to newer cubers when more advanced ones (</=12s) suggest practising them with the intention of improving lookahead.
When you get to the point of wanting to practise this stuff, I'd suggest practising a lot of different LL algs after copying pro level fingertricks, and practising scrambling as quickly as you can.
In regards to freeFOP, I would suggest studying a bunch of f2l algs to improve treading that line between pure move efficiency and occasionally teching in a 9 move tps-spam algorithm.