Here are some thoughts:
No matter if you stop or continue: There is never a limit. If you put in more effort you will perform better. That effort can take many forms though, from being online more to learning how the game works, to learning how fighting works, to optimizing your city, to optimize your game play to even spend real money... All those things will make you perform better if you stay where you are and they will also make you perform if you continue to play more chapters.
And since all these factors interact it is hard to predict what happens "all else being equal", because all else is never equal.
If you want my personal opinion, then yes mid chapter 15 is the place for optimum tourney results. With optimum I mean highest possible average score (as well as highest max score), not highest efficiency (say time spent per point, if you want minimum effort/big score go for a tiny catering city).
Your decision is based on a few wrong assumptions though.
1. The "swords" you refer to are unfortunately a blatant lie. They do NOT say anything about real quality of a unit, the best info you can get is, if a unit is Good or bad. But five swords does not mean better than say 3 swords. It is rather random and I don´t even know what Inno is basing their sword numbers on. I don´t think it even (exclusively, although it must have something to do with it of course) based on the bonus units get against certain enemies... Anyway: Bottomline: Forget the swords, base your decisions on better data that that! If you put OK data in, you get an OK result, but not a good one.
2. Maybe connected to 1? Merc Camp is not useless, not even with 2 star units. Of course 3 star is better than 2 star, but not every 3 star is better than every 2 star. The very best unit in the Merc Camp is the blossom mage, which is a unit you completely forgot to think about. Even at 2 stars it is just as good as the 3star enchantress and it will depend on the situation (mostly the terrain and the the type of enemy) which one will perform better. The 3 star upgrade comes in chapter 14.
In general I would agree that regular 3 star archers are better than 2 star rangers, but again, not always.
Frogs are very different from Golems and both serve rather different purposes, so it is hard to even compare them. Best to have both, even when 3 star frogs are available.
But ignoring all of this: Even if you were right that the barrack troops are generally better (which they certainly are not), you would still benefit from having a Merc Camp. The quality of the troops is not the only consideration. Quantity counts, too! And having a Merc Camp (and a Training ground) will double (or triple) your troop quantity. More troops = more points, especially at the low tourney scores that you are talking about. Quantity without quality does become less relevant once you get to really high scores though, but that´s a topic for a later discussion.
3. Timewarp (end of chapter 14): You miss the most important effect of the timewarp. The convenience is of course nice, but they real punch it packs is a different one: And this is why the TWarp in my eyes is the single most important AW for tourneys in the game:
If you level it high enough (and additionally use the help of a Polar bear) you can reach a state where your cooldown time is so short that you can play the entire tourney (all 6 rounds) in 1 day. That in itself is not a big deal, however the spacing of the tourneys allows you to play 2 tourneys within 5 days: 1 on Staurday and then one again on Tuesday (that is only 4 days total!) And that means that every 5 day booster building suddenly can be used for 2 tourneys, which in effect DOUBLES all your 5 day boosters effect! That is the single biggest step you can take to higher tourney scores.
So these are the reasons why I believe mid 15 is the best place to stop research. However it is of course possible to stop at various places before that at least temporarily. I for example had a 6 months stay in the beginning of woodelves, just after the barracks upgrade research. That is also my advice for stopping places: Stop right after a barracks upgrade (best if you can even get the Merc Camp upgrade as well nowadays). You get the increased troop production, which will give you a boost. From then on your tourneys only get harder for the following 2 chapters, until you get the next barracks/Merc upgrade. It´s like an upwards sloping zigzag
You get barrack/Merc in chapter 9, 11, 13 and 15.
As I said I stopped in 9 for 6 month (just after they invented PP spells and before they invented the spire), maxed out Needles and MM (plus Shrooms 16) there, but I still enjoyed my time parked there so I continued to upgrade GA, MH and PT there as well (although I might skip that part or at least keep them lower nowadays).
By the time I felt like continuing I had enough PP spells to short cut through all chapters till and including 15 (that took another 6 month). I haven´t moved since.
