The question is in the subject. This is true also for ignitors that pulsing at 50 pulse/sec and not only low frequency pulse ignitors.

Semiparallel ignitors generate way slower transients than the superimposed ones.
The ballast choke just has way higher leakage inductance and winding capacitances than the compact pulse transformer of the superimposed type.
Plus many superimposed ones actually generate multiple pulsed pedr mains half cycle, so ending up with way more "edges" in the ignition voltage, so producing way stronger capacitive corona (when the current does not return via the other electrode, but by the capacitive currents to the surrounding metal work) discharge increasing the chance of some of them to actually ignite the lamp.

And MHs are generally harder to start, require higher ignition voltage than HPS.

When you combine these two, you get this difference:
HPS strikes immediately on anything.
The superimposed with MH generates steeper and more edges, so it is igniting it rather immediately as well.
The slower and fewer edges of semiparallel then takes longer to strike the harder to start MHs...

So why HPS lamps restrikes faster with semi-parallel ignitors than with superimposed ignitors?

How do you come to this generalized conclusion?

I've seen that HPS lanterns with Eltam ES-50, Philips SN-58 and SKD and Tridonic APU semi-parallel ignitors, tends to hot restrike faster than lanterns with all brands of superimposed ignitors.
See how fast this lantern restrikes its cycling 100W HPS lamp, and it have Philips SN-58 semi-parallel ignitor. The same lamp would restrike after 30 secs with a superimposed ignitor. New HPS lamps may restrikes instantly on semi-parallel ignitor, compared to superimposed ignitor.

Looking at some random combos with some random lamps and ballasts of different ages does not allow you to make this statement. There may be old worn superimposed ignitors and also looking at EOL lamp behavior is equally useless etc etc...

And *please* stop now, don't drag us in the another pointless discussion as you like.

You have to do a controlled experiment with the same group of new lamps, aged to 100 hours, new ballasts, controlled line voltage (better off a power synthesizer), the same wire lengths, the same environmental temperature and lamp surroundings and so. This requires a lot of money and dedication? Absolutely sure. What to do? - Stop making unfounded statements.

 

One particular thing to bear in the mind is HPS lamps (except SDWs probably with their special electrode shapes and high pressure fill and also some very worn regular HPS) generally do not require very specific ignition pulse energies and repeat rates to do glow-to arc. Once the electrode gap is stroked through end-to-end completely, the proper discharge is initiated. This is contrary to MH lamps which always have quenching halide impurities in the arctube. So in the context of HPS restrike time, an ignitor with just higher HV  pulse amplitude will win, be it superimposed or semiparallel. To be honest, pulse frequency probably also matters for ignition threshold, but not much.