I was reminded of this thread yesterday when playing Bleed. You're not running (or forced to run) all the time in Bleed (the train level sort of encourages taking breaks), but it's pretty common. Some factors that come into play here:

• Autoscrolling segments: this is a no-brainer and lots of games have them, but they're at least worth mentioning.
• No pickups at all. No secrets either, unless I missed something, or keys and locks or anything like that. This is completely the opposite of Stijn's suggestion from the start of the thread, but it also means there's no reason a player wouldn't want to keep moving forwards at all times. (ETA: Although you could probably get away with pickups so long as they're in a straight line directly in front of the player, and maybe even disappeared if you passed them without collecting them?)
• Enemies weak enough for you to kill them before reaching them, assuming you aim correctly. A tuf turtle, unless you can jump over it, does not encourage speed. A lizard is fine.
• Danger from behind you. This feels like a big one, even though it doesn't show up in every level. It shouldn't be safe to stay in one place indefinitely.

So there are some surface thoughts. Bleed also puts a big emphasis on dodging through the use of the dash and time-slow mechanics, in combination with lots of enemy bullets, but it might be possible to separate out the speed from that? Idk.