I don't know why you're so hung up on semantics, but whatever. Point is, the GTA in Sol only had experience with Shivan heavy beams. The Lucifer's forward beams are all that wound up in Sol when the node collapsed, and there were no threats in Sol that required the GTA or UEF to build heavy beams, so they didn't bother trying to replicate them.
Yes, in hindsight, we know AAA beams are possible. The GTA/UEF didn't. In the absence of any threats requiring heavy beams, they had no reason to invest in the technology, and therefore no way to know AAA beams were possible.
The GTA outside Sol, however, did have a need for that technology. GTI adapted it first, and some time after Silent Threat, the GTA and PVE followed suit. At some point, they realised the technology could be downscaled and adapted to shoot at fighters. This, to me, is the most likely explanation for why the UEF has no AAA beams. If you have an alternative, do share it.
Who cares if the beams on the Hades were SSLs in tables? BP replaced the beams on the Lucifer with something weaker (LReds), and getting hung up on table stats is the worst way of discussing BP.
In a BP context, there's no reason to believe the beams on the Hades were carbon-copies of the Lucifer's LReds, or anywhere near as powerful.