Reading "1776" it seems like everyone else realized this was a good idea and the reason he didn't was because... he didn't feel like it!
It is very hard to answer the question, "Why didn't someone do something", historically.
Unless they left written records about their decision, we can only speculate.
Possibly, General Gage did not think that the Rebels had large enough artillery to make use of Dorchester Heights as a strategic location.
Indeed, they did not, until Knox managed to transport the big guns from Fort Ticonderoga over the snow to Boston.
Gage might have been unaware of this acquisition of heavy artillery until too late, and thus the Rebels fortified Dorchester Heights and mounted the cannon before he managed to take the heights himself?
Once the Rebels had placed heavy cannon on Dorchester Heights, Gage could only attempt to assault the position or withdraw from Boston. He mounted an attempt to assault the position, but a gale of adverse weather stopped the attempt, and he then decided to evacuate Boston.