The problem was roaming charges in Europe weren't always cheap, often required separate SIM cards and it was a pain to do. Doubly so when you consider how the different countries in mainland Europe are effectively borderless.
The EU only steps in when corporations have already failed to regulate themselves.
Corporations don't regulate themself. Why would they choose to regulate themself if that means higher cost or less margin or less business opportunities (like selling assault weapons to civilian population) ?
Market can bring prices down if competing corporations in the same sector don't agree to set prices for the same range of services of products. That's it.
Self-regulation _can_ work... if the state is standing there with a big stick willing to use it if the market doesn't regulate itself well.
As a case study, take advertising in the UK.
The Advertising Standards Authority is a Big Deal. It can ban advertising on TV, in print, on billboards and online. Its decisions regularly make the headlines.[0]
It also has no statutory basis, it's a private limited liability company, and they receive no money from government.[1]
In the general sense you're right however I think you're drifting into a philosophical point. Normally it makes more sense to let businesses have a certain amount of freedom to operate and only step in when necessary. The hard part is agreeing where "necessary" is. For example EU tends to have a different perspective to the US on when industries should be regulated.
US telecoms costs are insane though. Paying less than $50 is basically impossible for a decent amount of data (5+GB). Google Fi for example is $70 + tax
In the UK, it's hard to spend more than £20/month (for sim only at least)
Mint [1], is $20/mo for unlimited data (throttled after 8GB), using the T-Mobile network. You get a discount for committing to a time period such as 1 year.
Visible [2] is $40/mo for "unlimited everything" (data, calls, text). This is Verizon's low-cost product on their own network.
Simple [3] is $40/mo for 15 GB, also using T-Mobile. You're throttled to 2G after that, though.
These are MVNOs, which are resellers that don't own their own networks. Traffic is deprioritized compared to the parent network's "native" customers. In practice, you might not notice at all, depending on how you use it. Deprioritization really only happens during congestion. During rush hour on the NYC subway might be a time you'd be affected, for example.
I don't think lower population density explains it fully, for example Australia has extremely reasonable phone plans - you can get 15GB data/unlimited talk/unlimited text for AUD$55/month (USD$37/month) [1], and it gets even cheaper if you get 12 months up front [2].
The EU only steps in when corporations have already failed to regulate themselves.