No. The danger with "old" is that at some point on the aging curve a player is no longer physically able to function at that level. And at that point, Spurs would still have to pay for someone who couldn't be a part of the squad, but who might be unsellable given the contract we gave them. For example, look at Alexis Sanchez at MUFC. He has hit his decline, and is completely unsellable because no one on the planet is going to pay what he currently makes, so MUFC will need to eat his contract for the next several years while they won't get any reasonable contribution for that money.
Aging is not an exact science, and no one can predict when that can happen. The risks can often outweigh the rewards without a lot of medical data to give some context. So, mid-30s Luka Modric? At some point, his body is going to say stop. And no one knows when that is. But do we want to pay for that? I don't.