My assumptions are correct. You base
your assumption on the knowledge you as an American have of travel insurance and that is my only assumption. You think that coverage will be sufficient.
Let's say you are hiking in Spain. You lose your footing and take a fall. The result is a broken arm. Cough up 12.5k Euros ($15,300 USD). Your 10k Euro insurance, will come up short by 1.5K Euros and that is just for a broken arm. What if you do more damage than that and end up in hospital for an extended period of time and need more extensive surgery? You are going to come up short by a large amount.
The coverage you are talking about is actually decent Medical Evacuation insurance but it is lousy Medical Treatment coverage. The OP is not asking about just evacuation insurance, the OP is asking about medical treatment insurance. What is your answer to that? Nor is the OP the only person or nationality interested in this thread.
This is what you have a version of:
https://www.forbes.com/sites/everett.../#5053e5d34153
Depending on where you are in the world, an air ambulance flight to your home country can cost anywhere from $25k to $250k plus. That is indeed good cause to make sure you have coverage for that either as part of a comprehensive travel medical insurance policy or as a separate coverage such as you have.
My beef with your coverage is that it is fine for evacuation but not nearly enough for medical treatment coverage. You say, "It is not for routine medical care - that is what my normal health insurance is there for." What normal health insurance? What coverage does it give you outside of your home country?