In the tng episode "When the Bough Breaks", S1 Ep17, after the enterprise fixed the ozone layer, cured the people, and agreed to teach them about their technology and how it functioned, why didn't the federation gain their repulsion weapon technology that was able to send the enterprise three light days away at warp 9(and claimed to be able to send it much farther)(and any other advanced technologies they might have, ie the ability to cloak an entire planet for a millenium)?
The best answer I can find is from an interview from the TNG Companion (see below) in which it's stated that the original idea was that the power supply (for the repulsor) was simply a "little black box"; something unfathomable and clearly far beyond the Federation's own technology.
In the absence of any additional info (Aldea isn't mentioned at all in any further TV episodes and only tangentially in the EU books), we're left to conclude that the reason the Federation didn't replicate the energy source and repulsor tech is that it's either;
Too advanced (and that in the intervening decade they simply haven't been able to replicate it)
Inherently dangerous (note that Data describes the incredible energy potential, the known propensity for Aldean tech to cause infertility and the fact that they enter the Power Station with extreme caution)
This was another script in which [Rob] Legato [Visual Effects Supervisor] would provide an impressive yet inexpensive FX solution to a story need: the Aldean computer’s power room. “The script called for a ‘little black box’ power station, but that wasn’t enough,” he said. “It needed to be something that left you awestruck—but how, on a low budget?”
INT. ALDEA - POWER ROOM (OPTICAL)
They ENTER cautiously. In the center is a shiny black box, not very large. It PULSATES with a GLOWING LIGHT.
RADUE : What is it?
PICARD : The legacy your Progenitors left you, Radue. The source of your power. And your problems.
DATA : It is reading incredible amounts of energy, sir. Even more since we have taken down the shield.