Quite simply because à is primarily (as its root sense, before it began “diluting”) a locative preposition that is far more commonly found connecting two verbs than two nouns, and when connecting nouns, it’s usually because the expression derives from a verbal one.

You would not write mon expérience à unless you specifically mean experience acquired in a certain place as opposed to your global experience of an object/event/place.

I’m also still a student so this might not be the most reliable advice,
nonetheless, you’re asking a good a good question, the two prepositions are often confused by most
students. They can both vary significantly based on context.

Here are some examples:

*de is normally applied in instances involving the from or those including of,

e.g.

1. Je viens de la boulangerie (I’m coming from the bakery)
2. Lucas est un de mes amis (Lucas is a friend of mine)

Whereas à is usually used in instances involving: to, at or in propositions.

i.e.
1. Je suis à la maison (I’m at home)
2. Je vais à Toulouse (I’m Going to Toulouse)
3. Je vis maintenant à Paris (I now live in Paris)

I guess the best way to understand them better is to familiarize yourself with multiple examples comparing both under
different contexts, hope this helps, all the best.