Actually Bisq does not require you to always be online. You can connect, take an offer and then turn off your computer and come back later. You only need to stay online if you want your available offers to be visible (ie: you are a market maker).
Thankfully this will soon also be easier thanks to the new API which will alllow mobile apps to connect remotely to your Bisq node. That way you can leave a small computer with Bisq running and get notifications or place orders from your mobile app.
If you frequently trade on Localbitcoins... I highly encourage you to try Bisq on September 20th as part of the kick-start. It's only one day and you have little to lose.
Sorry OP, I should have clarified that yes, I'm generally a market maker when it comes to Bitcoin, which is what I appreciate Localbitcoin's functionality - I set the limits or choose to auto adjust and it's always worked fine for me. I generally only take offers from trusted traders.
That said, I have always kept an eye on Bisq, trying it several times, but I will definitely support this kick-start and perhaps even try it out on mobile (never tried the app yet) running up to Sep 20th.
If more people get behind a decentralized exchange like this and pick up on community based projects, we'll see bitcoin being put to the use that was actually intended for it--P2P exchange without being monitored or charged commissions. Bitcoin kind of lost its original intent a bit I think when it turned into another "get rich quick scheme" last year as everyone thought they could make a bunch of money off it.
I also use Localbitcoins.com mostly because its easier once you establish a relationship with certain people. But it could just as easily be done here too, and the prices are very reasonable.
I think it's quite all right for Bitcoin to find different uses. Power to those who would see it as an investment asset, store of value, or whatever. But yes, I think it would be a refreshing reinvigoration to see more people use Bitcoin the way it was intended to be. Strangely enough (or demonstratively perhaps?) we're now seeing people do just that because they're forced to, in economies that are increasingly pressuring people to seek alternatives for currency.