People may prefer cheap to expensive but that does not mean they are desperate.

Again, your conditional statement is doing a hurculean amount of lifting here. We know that healthcare is unaffordable for a large swath of our population, but are you implying that mental healthcare (which doesn't have nearly the coverage on most plans as physical healthcare) wouldn't be in a similar state? Because mental healthcare is out of the reach of a lot of people.

The option isn't just cheap or expensive therapy. No therapy is as much an option if the therapy quality was 90s level machine chat bot.

False dichotomy, the chat bot can be better than the 90s bots but still be bad. And 'no therapy' isn't an option for a lot of people who will self harm as a coping mechanism.

Why is it exactly a problem that people have an extra avenue to better mental well being?

Why is it a good thing that people are using a tool that will yes-and just about anything they say and lead to psychosis in patients with no accountability from the provider?