I don't see why every device out there ought to have an abort option for each and every stage of operation - and that goes for very dangerous devices, too. A hand grenade doesn't have one, once the pin is pulled and the handle is allowed to pop free.
It may simply be impossible to stop an already brewing Genesis effect by any means that are less destructive than the effect itself. Genesis is the mother of all broths: once Khan triggered it, the ingredients were already thrown in the pot, and there was no "countdown to detonation", there was merely an informative counter indicating how soon the broth would finish its unstoppable brewing. Essentially, detonation had already happened when Khan pushed in the last of the child-proof activation mechanism elements.
For deciding why the brewing was unstoppable, we'd have to decide how Genesis works. Yes, it may look like an unrealistically potent technology even for Star Trek - but essentially it looks to me like it's just a really, really big replicator let loose. Sort of like the relationship between the A-bomb and the fusion powerplant: it's easier to achieve the former, unregulated, uncontained effect than the latter, contained and regulated one.
If replicators are an outgrowth of transporter technology, an advanced sort of Trek magic we already accept as default, Genesis could be an earlier spinoff. And if the Genesis effect is an expanding transporter wavefront that performs the replicator trick on everything it encounters and transports, it makes weird sort of sense that phasers would do squat in stopping it. Phasers and transporters both seem to be "phasing" phenomena, related technologies (hey, both make people disappear to some strange realm!), and hitting the already unstable Genesis phasing effect with phasers could plausibly only create a further reduced state of stability...
Now, we only need to decide how the wildfire transporter effect could be launched by Khan, then be contained in a bottle for X minutes, and then be released to do its typical lightspeed expansion. And TNG technobabble already establishes that the transporter effect is indeed imprisoned in a magic lamp, the "pattern buffer", during routine operations. Blowing up the buffer of a standard transporter may not do much harm. Fooling with the buffer of a replicator may result in the sort of mayhem we saw in VOY "State of Flux", though. Damaging the buffer of Genesis thus could plausibly release the Genesis Genie.
Timo Saloniemi