You've already stated the fact British shows tend to have fewer episodes than their American counterparts (see here for a great explanation).
However, there are a few other things to consider when discussing Sherlock. From a Digital Spy article:
"[The format is] very closely held," [PBS Executive] Eaton told Collider. "Steven
[Moffat] crafts them, and Mark [Gatiss] writes some of them. It's a
lot of work, and [Steven] also does Doctor Who and he worked on
Tintin, so there couldn't be more than three."
Eaton argued that Sherlock co-creators Moffat and Gatiss use up all of
their "creative juice" on the show.
"I think there will only ever be three at a time, if we're lucky," she
said. "It's getting harder and harder to do another season, not just
because Benedict and Martin [Freeman] are getting such high profiles,
but Steven and Mark are busy and in demand."
So it does appear that, in addition to the excellent answer I linked to discussing the shorter British seasons, the fact that Moffat has so many other shows to look after means they are on a very tight schedule and don't have time for more episodes.
Also, to give more background on the schedules of Cumberbatch and Freeman, consider just Cumberbatch's acting roles since Sherlock began:
- Tinker Tailor Soldier Spy
- War Horse
- The Hobbit
- Star Trek Into Darkness
- 12 Years a Slave
- The Fifth Estate
That's a lot of production in a short period of time. Not only are the creators of the show busy with other projects, so are the lead actors.