Why did Otto Octavius use tentacles mounted on himself instead of remote controlled robots?

This was addressed in the official novelisation for Spider-Man 2. In short, Doc Ock was sick and tired of not having enough hands. They were inspired, it seems, by the humble octopus.

Octavius loved the design he had created for the arms. It had come to him one day after a visit to the Coney Island Aquarium: the answer to the endless frustration of trying to perform experiments and wishing one had more hands at one’s disposal. Thanks to the four actuators—which, he had to admit, sounded like the name of a singing group—a scientist could have all the hands he reasonably needed. And they weren’t even the main invention he’d developed. They were merely tools he would use to help get the fusion generator started up.

_{^{Spider-Man 2: Official Novelisation}}

In the 2005 5-issue miniseries Doctor Octopus: Year One, we learn Otto had been raised in the nuclear era, and thus, as a brilliant child, dreamed of bringing nuclear energy to the forefront, leaving coal behind. Somehow, this fascination became something akin to love, and so he created the arms, attaching them to his nervous system, in order to give himself the ability to feel radiation as basically a 6th sense.

I recognize that I am extremely late to the party, but as an amateur Doc Ock fan, I think I can answer this. phantom42 answered this partially, but I believe his source may have been expanded on, as his was published in 2003, and mine was 2005.