The backup in 2016 Essentials is MUCH improved, although the one in 2012 should be pretty much like the one in WHS, which I find to be totally transparent, I never see it, yet all my machines are backed up. And I sometimes am awake at odd hours so it's not just that I happen to always be away when the machine is backed up. I haven't used Essentials in any version, but for WHS, you can just pick any of the backups and mount it as a drive to copy files off - also doesn't matter that the backups are all differential, it automatically retrieves all the files as of the date of the backup you are trying to restore from. It also does an automatic dedupe, so that 15GB of Windows system files on each of 5 desktops doesn't consume 45GB of backup space.
And remote access is slow? Over what sort of like? RDP is pretty darn fast with almost no lag over the connection speed most people can get these days. Locally, as in over a LAN connection, it's utterly seamless. I probably do 80% or more of my job via RDP so I'm not constantly driving around to client locations (or flying, since I support clients as far away as Las Vegas, and I live near Philadelphia).
Granted I've been working with this since before Windows 3.1, but the WHS (and I can't imagine Essentials is any worse - it was designed for use by non-IT people) is absolutely hands off. Once in a while I may peek in on it to see how it is running, but the client will notify me if anything goes wrong, so there really is no reason for me to log in to it unless I want to add another drive.