In a lot of scenarios you'd want to keep it to split push. Which some could argue as very uniteractive as you're constantly threatening to take down a structure, more specifically inhibitors.
I'm not sure how that isn't interactive; in soloq, many top laners can't play tanks right now because of conqueror's prominence and the simple fact that tanks usually require teamwork to play with unless they get significantly ahead. Because of this, there are 3 main options: teamfighting carries, bruisers, or off-meta picks. Carries excel at teamfights, and in general easily beat out bruisers unless, again, the bruiser is far ahead. This means that the only option for a non-fed bruiser to have any impact is to split-push and be able to teleport once every 5 (or 3?) minutes. This leaves a wide window of opportunity for fighting when it is on cooldown, or since it has a 4.5 second cast time, they can easily disengage and reengage a few seconds after it is canceled. Otherwise the bruiser would be forced to sit in a teamfight and die over and over with no very little impact for the most part, until they lost. That doesn't seem interactive at all. Neither is pushing without tp, hitting towers every so often until you can be sure you have an opening, then going ham until the teamfight is over, at which point you retreat and do the same thing again and again. With tp, there is a choice which is otherwise unavailable, and is one that can and obviously does change the way the game is played.
But right now as it stands it ONLY used as a means to stay relevant in the game for how poor you perform.
You died and lost first blood? TP to lane, farm under tower - in a lot of cases very uninteractively
and get big and impossible to 1v1. Or mid to late game, you're still negative? 0/3? Keep farming lanes where no one is nearby until your team needs you. "Oh you guys have it handled and don't need me? I'll cancel and farm some more! It'll be up sooner since it's reduced cooldown."
If you get first blood and allow a champion to farm under tower without taking advantage of it, that's your fault for not being proactive and making the plays that need to be made.
- Start a freeze. Punish them if they walk up. If they get jungle help, notify your jungler to it and they will make a move. Otheriwse, you just won your lane if you don't make any stupid mistakes. If their jungler doesn't come, you can easily set up a dive with your own.
- Can't start a freeze? Shove and roam. Invade the enemy jungle (safely) or look for objectives to take with the rest of your team. Never sit back and play reactively.
- Just beat them right out. Don't let the enemy player get to late game by letting them farm it out. Chances are, if they're a champ that needs to farm to late game, they won't be strong early. Take advantage of it and punish them for any mistake, taking towers and other objectives when you aren't tilting them and making their lives hell just to try and get farm.
If you let them get to late game and no one on your team has made any extreme mistakes or fed the enemy a feast, you can only blame yourself.
Plus, if the enemy is 0/3 or worse and is still able to out-push you or counter split you, that seems like a you problem, not the game. They shouldn't be able to get priority and tp before you do, or possibly even tp at all if you are in a winning position.
What Riot is doing is just making it harder to keep farming when your team needs you the most. You can't flake out last minute because your team won 4v5 at Baron pit and now YOU, the TP user, gets to have a reduced cooldown for the next fight that breaks out where your team still most likely not need you.
A 5 or 3 minute cooldown is still easily able to be taken advantage of in anything but coordinated pro play. Respawn timers are 60 seconds at most before 40 minutes, and if you let a scaling comp that wins off of farming get to 40 minutes then that is entirely your fault. Either way, that's still at least 2 minutes to make plays around the map, which is exactly what you should be doing when a tp is down. Plus, if you're ahead, I don't see how you would lose a 5v4 teamfight in the first place if you actually play well and are ahead as you say.
All in all, I don't think tp is as polarizing as you say. Sure, it can help someone who's losing to not lose as hard, but it can also help someone that's winning to secure a win at just the right time. Either way, it depends entirely on your using of it, and the impact of each play that can be made both with it up and with it down.