Why are the 737's variable-speed generator drives so unreliable?
@Jpe61 is correct in his comment that it's likely an electronics issue, since indeed a VSCF is mechanically simpler.
VSCF is also used on the MD-90, with poor initial reliability[1] – MDC went back to IDGs for the MD-95 (717).[1] It's also used on the 777 (only for backup, also with poor initial reliability[2]), and on the F/A-18.[3]
Capacitors
The F/A-18 utilizes cycloconverters, while the aforementioned civilian applications utilize DC-links (possibly the voltage-source inverter type based on this patent by Sundstrand, the makers of the 737 unit).[3]

... when electrolytic capacitors are used, in the case of a voltage DC-link, there is potentially a reduced system lifetime (Wikipedia: AC-to-AC converter § DC link converters).

More here: Wikipedia: Electrolytic capacitor § Operational characteristics
Your link says &quot;the failure rate was just over 1 every 2,000 hrs&quot;. The 2,000 hours match the lifetime graphs in the article linked above (shown below). This being the culprit is supported by a paper on aircraft power generation:

The VSCF systems, apart for some noteworthy exception previously mentioned [referring to the F/A-18 and F-117A], did not get the same level of diffusion of IDG systems. This can be safely attributed to the role played by the PEC [Power Electronics Converter] (either ac/dc or ac/ac), which processes all the generated power and represents a single point of failure. Therefore, the PEC needs to be designed for the full-power rating and with high reliability requirements.[4] [emphasis added]




High load and cooling
Once you lose a generator, say running at 0.35 load, the other needs to pick up the slack and run at 0.7 load. The CAA's imposed limitation despite the redundancy tells us they don't trust the VSCF at high loads.


Source: airliners.net

One feature on the MD-90 is the air scoop for cooling the VSCF components. The more electronics are used, the more intricate cooling is needed (you can't just dip them in engine oil).
Maintenance practices
There's an official Honeywell video on installing the MD-90's VSCF with hints at improper maintenance practices, which would be a headache for an airline since the system is very niche with different tolerances.
Summary
So whether it's a 737 or an MD-90, the issues seem to be:

Cooling
Capacitors
Maintenance practices

Note that the technology hasn't become obsolete, at least academically: a 2017 paper proposes a &quot;novel DC-Link VSCF AC-DC-AC&quot; for the Embraer 190/195, from which:

Problems existed with the older VSCF systems in the past; however, the switched power electronics and digital controllers have matured and can be now, in our opinion, safely integrated and replace existing constant-speed hydraulic transmissions powering CSCF AC generators.


1: Douglas Jetliners, Guy Norris and Mark Wagner, page 85
2: Boeing tackles 777 power problems, 18 August 1999, flightglobal.com
3: Control of Power Electronic Converters and Systems, Volume 2, page 341
4: Madonna, Vincenzo, Paolo Giangrande, and Michael Galea. &quot;Electrical power generation in aircraft: Review, challenges, and opportunities.&quot; IEEE Transactions on Transportation Electrification 4.3 (2018): 646-659.