They probably didn't want to bomb the entire palace since there were innocent civilians who'd get caught in the crossfire. They also did believe that Pitou could reverse he nen hold on Kite, and wanted Gon to settle things his way as far as that was concerned. Netero is also a martial artist who wanted to push himself to his limit and find out how strong Meruem truly was which maybe why he only wanted a 1v1 with Meruem, probably also why he only took Zeno's help in separating the ant king and not in killing him(Zeno would've rejected that request anyways cause the Zoldycks are a smart bunch, relatively).
There's also a lot of inconsistency in the series to be fair, I mean, Meruem could have easily guarded himself against the impact of the bomb had he used his nen. He's literally the strongest creature on that land. He could've also negated the effect of the poison when he realized it but they had to kill him or Netero and everyone else present there would've deid in vain.
But as the other answer states, it is a shounen series and they had to settle it in the old fashioned way. As to why Ging or anyone else wasn't called, it was probably the only way the author could've extended the series. Almost all of the last part with the new chairman election and Gon's condition would've been completely removed from the series.