In my vocabulary, that's the root not the tip (I mention this since nodes regularly use the tip, but seldom the root).
When nodes perform the initial block download and verification, they start at that genesis block and work towards the chain tip, which is the most recent block.
For one-time verification purposes, there's no technical need to hold the full tree locally at the same time; each branch can be verified separately.
True, but bear in mind prune nodes can be vulnerable in the scenario of a chain split. And as blocks become exponentially larger, then chain splits tend to become both become more frequent and longer.
Also, once the validity of the full tree is established at a local node, little is gained from full revalidation. This is the principle which makes pruning possible in the first place.
You still need a full node if you are going to run a wallet or indeed view any transactions prior to your most recent block. Having only a handful of full nodes responsible for fetching data on all by the most recent UTXOs is a big risk.