Only makes sense to trade him if you've got another goalie ready to take his place.

And even then, I'm not sure it makes sense. Everyone's got their eye on Murray but he was worse than Anderson this year and the year before.

Before this year Anderson had been arguably the most consistently good goaltender in the league over the past five years.

"Just let him walk"? No the player has the choice of accepting a team offer (if they offer one). It's not the teams choice if a player signs elswehere.
Leafs can find much better value elsewhere than Brodie for 5.5m X6. Why even include Bracco in any NHL trade

Teams let players walk all the time, what sport are you watching?

You make it sound like the current team has the control of a UFA when you suggest "let" them walk. No, it's players decision. Teams don't allow a UFA to stay or leave.
Now I might agree that the Leafs will not offer Anderson a contract next June.

I don't think picks can be conditional on extensions anymore.

This is incredibly semantic, "let him walk" is a common phrase to use when either the player doesn't want to stay, the team doesn't tender him an offer, or the two sides can't come to an agreement. Don't be this guy.

I thought I remembered hearing they removed them as part of the new CBA extension but I can't find anything on it

Thank you!

That is news to me but I’ll look into it

I could be wrong, I thought I heard it recently but can’t find a source at all so maybe I was imagining it.

Never mind I found it. Google NHL CBA Changes. The 35 year old rule is gone now as well.