I don't depend only on my bike, but that is my preferred commute method.

A couple of things (assuming that your ride is not ridiculously long & your bike is in decent shape): As has been mentioned before, the more that you commute by bike, the more you will commute by bike. Same thing with any other form or tranport. It's a change, so it takes some getting used to. I don't ride in the winter, so come spring-time, I don't ride as often as I do in the fall because I'm not used to it. I need to get up earlier, leave earlier, pack, etc. In the fall, after I've been riding all summer, I will ride more often, even when the weather is colder than in the spring, simply because I am used to it.

2-Insomnia can have a lot of causes. One of them might be lack of exercise/poor diet. If your problem is not something that is an actual impbalance (Ex: it's caused by diet, exercise, stress, etc) the physical exertion of cycling should actually help. If you don't get sleep, then you're tired one day (Obviously don't do this if you truly can't keep your eyes open) make the effort to get up early & ride to work. When you get home, you'll be so beat that you should have no trouble going to bed at night. Once you are tired at night, insomnia shouldn't be a problem, and you may find that you feel better all around.

Don't take this the wrong way, but some of your issues sound more like excuses for not riding. Insomnia may or may not be a legitimate reason not to ride, but bad weather & sickness should not be happening all that often. If it's raining on the way out to work, or if they are predicting massive stomrs throughout the day, I won't ride. But the weathermen are incorrect often enough that the threat of rain later in the day does not deter me. And sickness should really not be a problem more than a few days a year. If it's more often that that, you may want to look at the causes. Same thing with working late, most of us have days when it's like that, but if your job is regularly requiring you to work till 2 in the morning, then come back by 8, that's a whole different issue. All in all, those reasons not to ride shouldn't add up to more than 1-2 months of the year, which leaves plenty of other days for riding.

In reality, you may just not like bike commuting, which is fine. Lots of times, we want to do things becuase we feel like we 'should'. If you try commuting & after a month or so are still coming up with reasons not to ride every day, then I'd probably shelve the idea and do something else. If you already have insomnia, no sense stressing yourself out about something else.