My understanding of LastPass (I am a user) is that you _do_ in fact have offline access to your vault. Your Master Password is also the encryption key. Did I miss something?
I was a paid user of LastPass for about a decade. I don't mind a subscription-based model, especially if there's cloud-syncing involved (I've evaluated the amount of risk I'm comfortable with, and cloud syncing is fine for my use case). Part of the benefit for a paid account is the ability to access your passwords when there's a network outage.
However, in the year before I left LP, they went down three times, at most for about 4 hours. Each time, I could not access my local vault, not through the browser extension, not through the Android app, and certainly not through the website; no matter what I did, it was nothing but errors, and their support was useless. It just would not work. That was enough to spook me and get me off their service.
I was complacent, thinking that no matter what, I could always see my vault, regardless of network status, until it actually hit the fan. I'm currently with 1Password, which is quite slick (their change on 2FA is what actually got me to give them a try), but I've killed network access to my devices and was able to access my vaults.
Just in case, though, I have KeePassXC as well. You never know.
1Password does support local storage, cloud is used for syncing to local storage so obviously in case of an outage you wouldn’t be able to sync updates. But you would be able to access and modify locally and then it would push when things came back online.
A local-only storage solution with your own syncing is by far the best way. Also, storing low security passwords (eg Netflix) in chrome / iOS keychain seems like a pretty safe trade off to me.
I'm still having issues convincing friends/family that the initial friction of a password manager and replacing all of your reused passwords is worth it at all.
Security is a battle of convenience, and we still haven't struck gold for the layman to have decent enough security hygiene.
Bitwarden is open source for both its clients and its server. I haven't tried it but it appears you can set it up for yourself at home and not use their cloud.