Ich habe noch etwas gesucht und im Netz ein paar Diskussionen zum Thema gefunden, zum Beispiel

https://forum.wordreference.com/threads/advan...

Ich bin aber nicht sicher, ob ich schon alles verstanden habe und was das für den Satz im OP bedeutet. So ganz scheinen mir die Antworten auf der verlinkten wordreference-Seite auch nicht übereinzustimmen.

[I hadn't seen #2.]

I haven't thought about this systematically, but I think you often get "to" after "there are".

In your example, there are some advantages to using balloons obviously means "using balloons has some advantages".

A comparable sentence might be "There are two sides to every question", i.e. Every question has two sides.

In both these cases "of" would be wrong / unidiomatic.

But I can think of other, apparently similar, examples where you can't use "to", and I wouldn't be able to explain why not.

From

Longman Dictionary Of Common Errors:

WRONG: There are many advantages of having your own computer.

RIGHT: There are many advantages to l in having your own computer.

the advantage(s) of (doing l having) sth:

'He described the advantages of renewing the contract.'

'The advantages of independence soon became clear.'

there are (several l many etc) advantages to | in (doinglhaving) sth:

'There are advantages to working in a supermarket.'

'There are clear advantages to such an approach.'

'Are there any advantages in appointing coordinators?'

Ich verstehe das jetzt so, dass wenn man several oder many einfügen oder ersetzen kann, dass dann "... to ..." verwendet wird.

there are some advantages to using balloons

there are several advantages to using balloons

EDIT:

Danke Hecuba für den Hinweis auf ... after "there are".

Sorry to disappoint you, but they’re both okay:

“The advantages of using balloons for surveillance are diverse.”

“The advantage of using a balloon for surveillance is that … .”

With both you could use “in.” I feel less happy about using “to” with them than with your Ausgangssatz. It’s a tricky corner. I’m afraid I can’t help with easy rules of thumb. ;-(

If 'there are' is present, you can't use of, only to/in. If it is not present, of/to/in are all acceptable. The same is true for 'there exist.'

Okay, das ist ja eigentlich eine recht einfache Regel, die ich mir merken können sollte. Meine Intuition will es zwar noch nicht einsehen, aber ich werde ihr in einer ruhigen Stunde mal erklären, dass Sprachen nicht immer logisch sind und dass sie - meine Intuition - hin und wieder die Logik nicht mal erkennt, wenn sie da ist.