Yeah always hit the deer, even though animal rights people would tell you otherwise, if you hit the deer and have comprehensive insurance they would have paid all the damage even if you had gone off the road and hit the pole.
On the matter of the ticket, it a catch all ticket, the officer can sight any number of reasons to justify the ticket, in your case the accident justifies the ticket, i.e. lack of attention caused the accident. Also the officer most likely wrote down your statement about your speed. Lastly, even if you hit the deer and the police came they would have written a similar ticket.
The officer comment about the speed and the damage is not relevant, they are not an expert, they have not clue how much force it would take to snap a pole. I have seen cars hit a tree the size of the electrical pole at 100 MPH and rip the car apart and the tree barely had any damage. I also seen cars hit a electrical pole at 20 MPH and the pole snap off especially ones with a transform on them since they are top heavy.
These tickets are generally are hard to beat since they are subjective at best, also today it is standard operating procedure to issue a ticket at ever accident. Generally an accident is something that may not have been avoidable, however, the government is more interested in assigning blame and making sure they collect money from you.
You could fight the ticket, and if the officer is a no show then you could most likely get it dismissed. A lawyer can most likely win this for you. Consider this, yes the lawyer will cost money, but far less then what your insurance will increase due to the accident and ticket.
I am not a lawyer nor am I in law enforcement,
I will not make any value judgment on why you're asking a questions.
I will try to provide information so you can make an informed decisions so take it for what is worth and do your own research.
Remember it is easy to tell someone they will lose verse providing knowledge.
Lastly, I have no vested interest in your outcome win, lose or draw and the same goes for anyone else.