Good old days? You mean like Diablo 1? D2 was online as well, except it stored your character files locally (so people could cheat their characters with a utility like Jamella).
I was mistaken. Still a long way to go back for an offline option, so it's probably a pipe dream in D4 and beyond.
I didn't mean that to sound as aggressive as it did, I apologize lol.
D2 could be played offline, I had a 28k connection when it released so I generally would just play it offline. I think regular Bnet was pretty good for not having cheaters but Open Bnet is where you could use your offline character and load him up with stuff using a trainer/program and play online.
At least in 3 you could choose to play solo which was way less laggy than this open world mess and most important of all you could fucking pause the game.
Being in a nightmare dungeon with one of a throusand affixes that force you to move at all times or you die by some shit that's constantly chasing you and then the door bell rings is great. Just great.
I've noticed it seems particularly bad during helltides. Best way I've found to fix it is close game and sign back in. This does suck if you're doing solo NM dungeons.