When I see the enemy team sprint out of their base to chase my 4 team mates and I TP to a minion in their base and fart on their nexus. When you lose game's because suddenly the enemy just appears in your base and ends the game is a real clutch that too many people aren't prepared to protect against. When someone says "Someone stay and defend" It's usually at the point where 1 enemy has the potential to enter your base and end the game, thus being very good advice.
I got trashed by a Yasuo top with Flash Ignite as a Darius top TP/ Flash. I really didn't try to but gave up first blood (I think I was half off guard Kennen was support and their yasuo was top and had ignite) I TP'd back ready to finish Yas off since he was weak, and didn't realize before it was too late he was level three and I died, again I was lvl 1, and dead, and lvl3 Yas was moving in on my tower. So yeah he won lane. But I stuck in, and after I grabbed Hydra built health into Sunfire and Frozen Mallet, and grabbed a Thornmail. I was able to solo 1 v 1 Yas and with really good team work we turned my embarassing start into a fantastic finish.
At my roomate's encouragement and my team's understanding, I got my crap together and front lined us to the victory screen. I was both the reason my team could have lost and why we won. Because of my mistakes early game and poor decision making, we coulda lost. And the fact I did not rage, or let myself get discouraged, I didn't cause my team to basically be 1 man short but staying useful and relevant throughout the game. I've won games where our "feeder" would get things together in the end, and I felt like we won because of the simple fact they found their zone and got back into it, rather then of how good me or my other team mates did.
TP basically plays a large role in influences those factors I just mentioned. The more team work you have with your team the higher impact TP has. The less teamwork the less impact your spell will have. With absolutely no team work you'd be completely better off with another spell entirely. Since you will prolly die any where you TP to, and leave any place you TP from vulnerable without you there.