Most Utility companies are basically monopolies. So why do they continue to advertise?

In Illinois, ComEd is raising our rates between 20% and 50% starting on January 1. Since I don't have a choice, I have to get stuck with paying the bill no matter how much I hate this because there is no competition.

Why is it that ComEd continues to put up billboards, TV commercials, and even buy space at the United Center (where the Bulls play) if we cannot pick another utility company anyways? When I see these, it just makes me more upset when I have to be reminded of my rates going up.

Some customers may have a choice, in many areas consumers have a choice of supplier. Or if not it may be under consideration. Commercial users may have choices also. The ads are to build a brandname recognition with customers, politicians, regulators, enviromentalists, suppliers, investors, bankers, etc. As far as the Bulls....maybe it is the luxury boxes and chances to meet players ?
And so when they raise rates people don't get too upset.

They're trying to maintain good will with the cities so their stockholders make more money on dividends. It's also the reason they don't take care of infrastructure like maintaining stations and burying the stupid lines so the power goes out and people die.

Utilities have been or are soon to be deregulated. I think they are getting ready for that deregulation.
What that means in particular to you, the consumer-- is that prices will probably be going down in the future. What it means to the utilities is that they must ramp up their production ( and build efficient power production) in order to survive-- look up the rolling blackouts in California some years back and what were causes for that situation.
What it means to me the investor-- my local utility has to compete with others in the production and transmission of electric power in the most efficient way. My electric utility has invested in and built windpower towers and clean coal fired plants that are producing enough electricity to sell to other electric utilities. It also has DRIP programs and easy entry into investment with them. I live in a warm state-- few forgo air conditioning-- The more efficient the better-- at the worst, my company will be bought-- I still am OK.
My initial plan for investing in utilities-- local so I can watch them-- and enough invested that when I retired I could withdraw from those companies to pay my bills from them. It is working.