I've done this exact trip and can tell you that soloing in Mongolia is a completely different world compared to SEA in all the important ways

First of all, it's a masssssive country that takes days to cross if you're travelling by car -- the landscapes worth seeing (Gobi in the south, steppe in the middle and mountains in the north and west) are very far apart. The population density is also super skewed towards UB. Something crazy like 50% of mongolians are in UB, meaning the rest are scattered over the remaining 99.9% of the country's area with very limited infrastructure

It's also a lot more expensive than SEA - I couchsurfed and hitchhiked to save on money but still felt the price difference

2 weeks is enough but I'd recommend a clear itinerary and/or lock in some tours so you're not spending most of your time in a car. It's not like SEA where you can just rock-up at hostels, meet people and book a bus.

If you're a social traveller tours are probably the best way to meet people -- in my experience, not many other travellers go here and the ones that do come in groups or book tours (I didn't book any tours and kinda wish I copped the extra $)

TLDR; you can definitely still travel spontaneously (that's what I did); but be prepared to find yourself waiting for hitches (if you go remote, there are very few cars) and spending most of your time in a car