I often use that move order. I've never found any disadvantages.

I also like to play 3 c3 against 2...e6.

I'm finding that 2...g6 is becoming problematic. I always used to play 3 c3 but the theory has expanded and I'm finding it hard to keep up (and remember!) it all, especially after the trendy 3...d5. I've looked at 3 d4 cxd4 4 Qxd4 but I'm not convinced it's anything for White. So, since I don't find that I play the white side of the Maroczy particulary well, and I don't want to risk transposition to a main line Dragon, I've been investigating the rare option 3 Bc4!? Bg7 and only now 4 c3, covered in Gawain Jones's book. 

Of course the main problem is that you can't get a 'real' Alapin after the most popular (in my experience, playing over the board mostly against opponents in the range 1800-2200 ) 2...d6, although there is no shortage of Anti-Sicilians then to choose from.
I tend to mix it up between
a) the 3 c3 Nf6 4 h3 Kopek
b) 3 Bb5+
c) 3 Bc4
d) 3 d4 exd4 4 Qxd4
e) 3 c3 Nf6 4 g3!? aiming for a King's Indian Attack - a particularly useful line against an opponent who you know likes to develop his knight to e7 vs the KIA.

I find the Quality Chess "Experts on the Anti-Sicilians" book from 2011 is still a very useful reference on most of these.