Not really. The biggest problem is getting more of the participants of the network bootstrapped with a fully validating node. Most people right now choose to rely on others instead which defeats the purpose of Bitcoin and makes the network overall insecure.
The chain is, what, 200 GB now?
It was for me for a while - I refused to download the entire blockchain. With that said, there have long been mitigations for end users with local wallets.
Yeah, I can't run a node without 200GB+ of free storage space. No way I do it on the phone for example.
You can bootstrap a node without storing the blockchain. You have to download it though to build up and validate the unspent transaction outputs which are < 1 gb iirc.
I run a node on a raspberry pi. You don't have to store the blocks after you validate them, it's called pruning.
It isn't even close to a big problem. Better design is great, but anyone who can watch youtube can still sync to any current cryptocurrency chain. Most people never will though, since there isn't much trust involved in using a chain on a server.