Not accurate. TM already had a lock the market before LN acquired them. In fact, LN created their own ticketing platform to compete with TM... and failed miserably.
Take a look at the largest venues in the country. Most of them aren't owned by LN, but they still use TM for ticketing. If anything, TM has helped LN to acquire more venues than the other way around. In general, TM has a much more dominant share of the ticketing business than LN has of the venue or promotion business.
OP asked why nobody has beaten TM. The answer cannot be "because they have a vertically integrated monopoly" because in the past that wasn't true and nobody was able to beat them then either.
Even if a venue isn't owned my LN, they still use TM for ticketing because otherwise their booking agents won't be able to get the Clear Channel artists to come. It has been that way for a LONG time. Before LN, it was CC.
Source: I used to own a night club in San Francisco.
"Founded in 1996 by Robert F. X. Sillerman as SFX Entertainment, the company's business was built around consolidating concert promoters into a national entity to counter the oversized influence of ticket behemoth Ticketmaster."
It's kind of amazing how the present distorts our perspective of the past.
So LN's market share in venues and acts is smaller than TM's market share for ticketing, and LN tried to use their venue/promotion business to launch their own ticketing platform and couldn't compete with TM... but right now the only reason people use TM is because of LN?
Surely, if LN's dominance is what is needed to lock up the ticketing market, LN's ticketing platform should have been able to compete with TM quite well, and TM should have been struggling to succeed in the ticketing market prior to being acquired by LN.
It's not that LN owns the venues, but that the venues have an exclusive ticket agreement with TM. So if you want to perform at this venue, you must sell via TM. When my startup was trying to compete, we found that basically every single outdoor amphitheater had exclusive ticket rights. This makes stuff like crowdfunding a concert impossible
Take a look at the largest venues in the country. Most of them aren't owned by LN, but they still use TM for ticketing. If anything, TM has helped LN to acquire more venues than the other way around. In general, TM has a much more dominant share of the ticketing business than LN has of the venue or promotion business.