If you've just come out of a successful Teamfight and are starting to push
Let your champions life steal/spellvamp off of the minion waves so that they can get back to full health. Was just going over a recent loss of mine to try and learn what went wrong and came to realise that we could have won if I had been able to life steal off of minions as we pushed up to the turret. Their ADC?, Support and Mid Laner were all dead and were on a 45 second timer by the time my team had gotten to the Inhibitor turret. I saw warning pings being spammed as they advanced and remembered that it was me who was spamming them because I wanted to life steal off of the wave, instead my team cleared it before I could get there. The jungle minions were gone and I was on 150 health, had I been able to get the wave I would've been almost back to full and we could've closed out the game. But I couldn't and my team was pretty awful, so instead we only got an Inhib and eventually lost.
It's a pretty specific example, but still, taking towers with a healthy team is better than taking towers with carries that are low.