Is the T-Shirt industry over saturated? In a sense, yes. To various degrees and different stages it is over saturated and over crowded. The industry is effing brutal.
Does this T-Shirt industry over saturation mean that you should not enter the highly competitive tee market? No, not at all. The problems lie with the lack of originality and the powerhouses crushing startups...be it manufacturing, distribution, or even retail. They (the powerhouses) do it by blocking, or by taking other people's ideas.
From the designer's perspective, it also comes from everyone having similar ideas or people blatantly ripping off other people's concepts. The same thing can be said about T-shirt Blogging, everyone tries to do what everyone else is already doing. The key is to be different and if possible, protect that difference with everything that you have. But that is a daunting task if there ever was one, if not outright impossible to achieve.
T-shirts may not make you rich, but if you enjoy it by all means keep at it. If it brings some income fantastic. Just be original. If you aren't making any money and that is your primary goal then it is pointless to continue.
How To Compete In the Over Saturated T-Shirt Industry.
To compete and make it in the saturated T-shirt market, look at the trends. Look at them and ADAPT to them. Don't just do what everyone else is doing but produce a variation that goes off in its own tangent and niche market. Avoid the self promotion label/logo tee crap like Old Navy, Abercrombie and Fitch, and American Eagle do. In all honesty no one gives a damn about your name or start-up brand. Why the Hell should they pay to advertise you? Again, BE DIFFERENT. Give people what they want not want you want. You may like your drawing of Deadpool wearing a Superman cape, doesn't mean others will or will not. Go for what you know for sure that people will like enough to buy.
That is my opinion on how to handle the T-shirt Industry being over Saturated.