This might depend on the country for EU. In France especially if you're an adult, getting an appointment for a diagnosis is either extremely long (public health sector delays regularly exceed one year), very expensive (over a 100€ out-of-pocket) or downright impossible (if you're in a big city you're fine, some places don't have anyone available at all). Sometimes it's a combination of those (yay).
And then if you're getting medicated, another whole world of fun begins (restricted prescriptions, shortages, etc)
You're talking about Paris here, not France. Even 'big' cities like Rennes or Nantes I never had to wait more than a week or two, and in the small city I live in I usually get appointments within a week (but I'm in a high QOL area so we might have a large concentration of specialists), and never out of pocket. But yes, in some areas you will have to drive up to two hours before finding a specialist.
Hey this is not my experience. Getting an appointment for my daughter - in France - was a few weeks wait. But also the whole diagnostic was around 500€, barely touched by the Sécurité Sociale and totally reimbursed by the insurance (mutuelle). This was in a minor city.
My understanding is that you typically pay something like this in the US for a specialist visit even if you have insurance, especially if you haven't already paid the year's deductibles.
And then if you're getting medicated, another whole world of fun begins (restricted prescriptions, shortages, etc)