That’s the exact definition of a “citizen’s arrest” - you have to be right there and see the crime happen to make the arrest legal.
That being said, cops actively discourage people NOT to make citizen’s arrests, as it can go wrong in a hurry ... what if the burglar knew kung-fu or MMA moves?
Cops discourage it yes but they dont have a leg to stand on because 99.9999% of the time, they put zero effort into investigating this stuff and finding out who it was.
Street cops are not generally “investigators” and detectives have little time or motivation to solve this sort of thing. Many think it’s beneath them almost.
So unless the perp is held until they get there, he will get away only to return again and again.