Why weren't SA-On GPS units updated to become SA-Aware?
As the linked ICAO article on GPS accuracy states, the issue is not just the navigation accuracy but the reported accuracy which is critical when used for ADS-B.
From the report:

3.2.1 For GPS receivers which are not SA aware, the accuracy and integrity REPORTED and then used in ADS-B messages is based on an
ASSUMED value of UERE, corresponding to the period when SA was active.
This value is grossly larger than the accuracy of the positional data
delivered now that SA is inactive.
3.2.2 For SA off/ SA aware receivers, some report accuracy and integrity values based on the assumed UERE in the SA inactive
environment and some determine the UERE from the GPS message contents.
Thus SA aware systems report more realistic accuracy and integrity
values.

When SA was on it was implemented by dithering the satellite's clock and ephemeris data to create a UERE of approximately 32 meters. So there was no attempt in the SA On receivers to compute the UERE as it was basically fixed by the implementation of SA. Remember this was first implemented circa 1990 and ADS-B efforts were in draft form when SA was terminated.
Also GPS standards weren't revised just because SA went away. The changes were primarily driven by SBAS and GBAS development efforts not the need for ADS-B. SBAS was the basis for the TSO-C145/C146. The air transport market wasn't very interested in SBAS, they tended to lean towards GBAS (if they cared at all.) The TSO-C196 (SA Aware) is very much like the C145/C146 units but without SBAS. (I'm not really sure of all the history of this TSO as it was after my time working these products.)
Product changes around TSO changes are a fact of life. Trying to upgrade a product from one standard to a new one just doesn't happen as it is by definition a major change and requires a new certification. And even with a new GPS built to a new TSO, it can't be swapped into the aircraft without an STC and that's a major expense.
So, could the original TSO-C129 units be upgraded to be SA Aware (without going to the new TSO?) Theoretically they could, but not economically. Computing the real-time UERE has to be done within the GPS chipset which would require a complete redesign of the custom ASIC at which point it just worth moving to the new standard.
As for the preflight authorization requirement for the SA Aware (C196) units; it's because they don't have the SBAS integrity channel. They rely entirely on an aircraft based integrity process. This can cause periodic cases where the integrity is reported as unacceptable.

Glossary:

ICAO: International Civil Aviation Organization
GPS: Global Positioning System
ADS-B: Automatic Dependent Surveillance - Broadcast
SA: Selective Availability
UERE: User equivalent range error
SBAS: Satellite Based Augmentation System
GBAS: Ground Based Augmentation System
TSO: Technical Standard Order
ASIC: Application-Specific Integrated Circuit