I get this take completely.
The Colosseum is one of those places where the idea of it is amazing, but the actual inside can feel a bit underwhelming for the price, especially when it’s crowded and rushed.
And yeah, €50 each adds up fast. That’s a big chunk of a budget, especially if you’d rather spend it on food, wandering, or other experiences.
The outside + walking around the area (Forum, views at sunset, etc.) already gives you a lot of the experience. Some of the best views really are from outside anyway.
I know people who went inside and loved it… and others who said “glad I saw it, but wouldn’t do it again.”
For a first trip on a budget, I think your logic makes sense.