I recently moved to the St. Louis area, so my experience here has been limited. Previously, however, I was active duty military in Altus, OK. I was a SKYWARN and an EM volunteer for the City of Altus. The lack of participation was a true problem there as well.
That said, the system, albeit in need of a few tweaks, was a very good, stable system.
In Southwest Oklahoma the SWIRA net (South West Independent Repeater Association) would typically stand up first. This net of linked repeaters was monitored by OUN (WX5OUN)
Following that, the Altus EOC would be staffed with the Emergency Manager, and Altus SKYWARN Association personnel, who would stand up the WX5ASA net.
Within the EOC there would be one Net Control for the WX5ASA net whose secondary function was to monitor APRS and position spotters, and one Radar operator whose secondary function was to monitor the SWIRA net, and relay relevent spotter reports to OUN via the SWIRA net.
This was a fairly well oiled machine, with the biggest problem being a few poor attitudes here and there and the typical lack of participation, but ultimately, it got the job done successfully every time.
During my tenure there, we never did fix the participation problem, but I guess thats thanks in part to the size of the community.
As for adding an extra step, in the world of radio, you're talking very minimal time. From the time I spotted something, to the time OUN knew about it was the time it took for two people to key up and say the report. I'd bet money this is faster than you digging out your phone, figuring out which WFO you need to speak to, dialling the number, explaining to the person where you are, and then explaining what you see. Not to mention that doing it over the radio in turn notifies any others listening in to the frequencies, which MAY be just the person who needs to be warned! If the EM needed to sound the siren it would be done the moment the report was heard in the EOC.
Additionally, regarding sounding the sirens, procedures are in place for what criteria are to be used to sound the sirens. Upon receiving training and understanding the times in which it is required, the SKYWARN net control/radar operator as well as the EM duty officer would be given the code to do so, for redundancy's sake.
I love HAM radio. Until the FCC eliminates all amateur frequencies, HAM radio will exist, because it involves so many aspects, not strictly SKYWARN/ARES/RACES etc. Whether it's place in storm spotting/chasing/EM etc.. is disappearing is definitely arguable, but as of now I still see it as a very valuable tool, that should not be written off.