There's nothing wrong legally with being a monopoly. Using your monopoly unfairly to perpetuate that monopoly is illegal.

So it is not illegal that one company handles such a huge percentage of ticket sales, or that they charge such a ludicrous fee.

However, if eg you started a rival agency and had a venue/event willing to use you, and then TM stepped in, offering ludicrous venue/event -benficial terms, eg, paying the venue 5x face value per ticket as long as the venue continued to use TM from then on, and then gave away the tickets for free, that probably would be illegal. It would make no business sense for TM to offer those terms for that event - they would only do so to kill off the competetion and lock in the event, and could only fund it due to the strength of their monoploy. Ala Microsoft/Netscape.

I hate TM fees too. I remember when the whole concept of outsourcing ticket sales was a fairly new idea. In many ways it was (and still is) a god send in convenience. Before you'd have to contact the venue directly to buy tickets. Today that wouldn't be a huge issue, but trying to find the phone number for an obscure venue in a distant city whose phone book you didn't have could be interesting. And then you often had to phone multiple times, firstly because every venue seemed to have different box office opening hours, and secondly because they only seemed to have 1 line and it was constantly engaged. And after all that, they still usually charged you some random fee to cover postage etc., although it was usually a more reasonable figure, 5-10% of face value. (Often you'd only pay one fee on a handful of tickets though).

TM take all that hassle away. In one respect though, it's not a good thing; True fans have no advantage over the masses any more. If a well known band is playing a relatively small venue today then it can come down to ping times or dialling speed. In the pre-TM days you could usually increase your chances with some effort, eg postal ticket requests were often allocated separately or handled earlier. Usually queuing outside the box office for a few hours could guarantee a ticket too. (As long as you got the right day )
TM has taken most of that away.