Actually, it's over 300GB for Bitcoin and almost 85GB for Monero today.
Regardless of that, I recently synced Monero from scratch in 3 hours, over a 802.11n network that never seems to do better than ~75Mbps. We can extrapolate that Bitcoin would be done in something like 9.5 hours. So I don't know where you got a week from.
If you still don't like that, you can always use a remote node, in which case you can begin using a new account literally immediately, even better than your 30 minutes at a bank.
IMHO that is a perfectly fine tradeoff for a new user who doesn't want to commit to syncing the blockchain. Nevertheless, when I deal with new, non-technical users in the Monero community, I find that they almost always prefer to run their own fully synced node, even though they understand the tradeoff (i.e., that using a remote node is probably fine). I even had a guy that has no computer, phone only, looking for help on setting up a full node on his phone.
Anecdotal perhaps, but it certainly makes me skeptical of the claim that blockchain size is a big hurdle for many people at all.
Oh yeah, and just for completeness: you can prune the blockchain with both Bitcoin and Monero if storage space is a concern, reducing it by something like 70%.