4000 dpi at 1080p is reasonable, If you were say, playing at 1440x900, that would've been going a bit over the top.
You can definitely get become a good player at that sensitivity, but from my own experiences and talking to expert high dpi players, it is harder and takes longer to build up accuracy and consistency compared to low dpi and large arm movements. As you probably know, high sen. is the only way to play with hand movements, I'm pretty sure everyone who plays at lower dpi use arm movement so you may as well disregard their advice.
So, if you like your playstyle then stick with it! but know that it will make it somewhat harder to progress, so don't compare yourself to other people, just concentrate on getting better. Also check out this guy
https://osu.ppy.sh/u/salochinOk as for tips;
-you really need to focus on accuracy. Speed is useless, passing the Scarlet Rose with a C won't count for anything, you need to be able to full combo songs with 98% accuracy to get good scores. So what I recommend is you start playing hards instead of insane mostly, only play songs that you can or are trying to full combo. It's taken me a full 6 months to be able to even full combo some hard with a degree of reliability, but of you want to be good it's what you have to do; you need to train your brain not to miss, when you play fast insane songs it's not beneficial for your skills as you're teaching yourself that you only have to be accurate enough not to fail that song. So I will repeat, focus on getting full combos, not passing hard and fast songs.
-Make sure your osu! sensitivity is at 1.0x, your windows pointer speed is at 6/11 with pointer acceleration off, and tun raw input on. These just insure your cursor is precise
-Get a mouse pad! going from a gaming mouse pad from a generic cloth one actually made me improve by a ridiculous amount. At high sensitivity it can really can make a difference, you don't notice it when you've got used to it (I only noticed after trying a tablet for a while), but playing on a surface with a lot of friction can make it way harder to make the small and precise movements needed. I recommend the SteelSeries 4HD (what I got) or the Razer Goliathus Control Edition (actually faster than the 'speed edition'). And if you haven't already, get a gaming mouse, they have low friction feet.
Anyway, good luck;
GANBATTE~