You can't just do that. First of all, you can't even tell what outputs are spent in Monero. Trying to remove spent outputs to prune the chain is very difficult.
People pay to have their funds stored indefinitely in monero, via debasement with the tail emission. Unlike bitcoin, where holders free ride, in Monero we lose some value over time as compensation to the network for storing our unspent outputs forever.
The security model with blocks missing from the beginning of the chain is not the same as with them. You might think this is no big deal, but it does fundamentally change the model.
These sorts of schemes have been proposed before, even before Monero. We didn't have this feature from the start because people didn't agree with it.
Dropping whole blocks globally is no good. Locally dropping blocks that a user doesn't have transactions in is fine, and we already do that (pruned nodes keep some subset of the rest of the blocks to ensure that a complete copy of the chain is out there, distributed among the nodes). So we already do something like what you're proposing, except nobody is forced to do it. If you've got the space for the whole thing, good, if not, run a pruned node.
Chain growth is a problem, but it's not such a big problem that taking a hammer to the protocol and consensus is worthwhile. What you're proposing is a drastic, not well thought out thing. We are better off chugging along until we can figure out some way to get full privacy without having to store spent outputs. We are very close to it, already MW exists that gets us ~80% of the way there.