oftentimes a given job (and this doesn't just apply to soldering, but to the practice of taking everything in your life apart piece by piece, measuring it carefully and then putting it back together again OK I HAVE A PROBLEM OK?
I GET IT) requires a combination of tools. heat'n'pull is a great way to get the component out initially. now you have a blob of solder, and if it's thru-hole, possibly two sides to get at it. this is literally the perfect time for a pump like the soldapullt, heat one side with your iron and suck with the other. DONE.
in the process of doing this, you very possibly used an adjustable vice or two, coarse tweezers, some gloves (burning onesself on one's iron sucks!), a good temp controlled iron, etc. etc. etc.
this is the excuse i use for owning so many tools.