Q:

In Season 6: Why does Qyburn take this approach?

In Game of Thrones season 6, what is the significance of Qyburn's 'little birds'

 murdering Pycelle?

Making him perish in the wildfire would have been less complicated.

A:

There's nothing explicit spelling it out that I'm aware of and no giveaway line, but killing Pycelle and not letting him go to the sept is perfectly in character for the methodical, calculating Qyburn we've seen up until now. Doing it the particular way he did fits a new side to his character that appears to be emerging and is suggested by other scenes.

There's one clear difference between Pycelle and those who were at the sept: Pycelle was the only also in a high position in King's Landing when "mad king" Aerys originally ordered those caches of wildfire to be placed.
He's very likely to know something about the caches, and therefore might pose a risk to Qyburn and Cersei's plan. Qyburn is generally methodical, cautious and measured. It's in character for him to ensure that a risk was dealt with.
What sort of risk could Pycelle pose? It doesn't require much imagination, especially considering that Qyburn's plan relied on children who might make mistakes. Pycelle's the only person likely to see the significance of, for example, a child being spotted running into a certain tunnel, a faint whiff of something few would recognise as wildfire, certain noises echoing from an improbable position below the sept. 
Pycelle's also the only character likely to notice his enemy Qyburn's absence from the trial (in fact, he's been the only character at court other than Cersei who has seemed to pay any particular attention to Qyburn at all - certainly the only one who has shown any signs of recognising Qyburn as dangerous). As viewers, it's also easy for us to imagine how Pycelle might have responded to Margaery's concerns: "And that madman Qyburn is missing too. Wait... madmen... the Sept... This sept might not be safe! There's a certain... ahem... vulnerability to this building... dating back to King Aerys... That devil Qyburn, it wouldn't surprise me... I can explain later... We must leave!". 

There's also a possible element of simple sadism. Cersei took personal care of a particular individual who had particularly angered her personally, and so did Qyburn. Having the two characters mirror each other like this, with Cersei relishing the sadism and Qyburn claiming to do it reluctantly, helps the producers frame this as jointly Cersei and Qyburn's work, giving us a glimpse of what their reign will be like, making it all the more chilling when we see them side by side in the throne room at the end.

As for why with children - as discussed further here, he seems to be training them to be more than just the 'little birds' Varys used. Both him and Cersei seem to be proactive in finding and eliminating dissenters (see, for example, the early scene where Clegane kills someone for mocking Cersei). When Qyburn smirks next to Cersei in the throne room, it's more chilling still knowing he has a network of murderous child-spies, like a Gestapo to Cersei's tyrant.

A:

This scene comes from the books, and it is Varys who does the killing. No doubt the writers and producers for the tv-show thought it was a great scene to include. (Which it is) 
As for your question about "Why this method?", the answer is, most likely, because of artistic reasons mentioned above. Any in-world reasons would be speculation, and most likely include some of the things that user568458 describes in his answer. Personally I would assume it is part of Cersei's coup de grace after Tommen's death. She killed everyone else, why not Pycelle? Although since Pycelle has always been on her side (and the Lannister's side), it makes less sense.
In the books it was, like I said, Varys who did the killing. Varys first bludgeoned Pycelle to death, and then shot ser Kevan Lannister with a crossbow. He used a crossbow as an homage to his brother (Tywin) who died that way. As for why he finished him with the children, who knows. Most likely just to demonstrate to the reader that they actually exist, and they are the "little birds" he has been talking about since book 1. I assume the crossbow and children as backup also has something to do with Kevan being armed and possibly dangerous.
Varys was already in two places at once in the season finale, so he could not very well be in yet another place. His motive would be to pave the way for Aegon by removing strong leaders who could oppose Aegon's claim. 
The scene makes a lot more sense in the books, where it shows us what happened to Varys, who had been gone since Tyrion's escape from King's Landing. And the connotation that Varys is supporting someone other than Daenerys includes a hint towards the Blackfyre theories, which are largely ignored in the tv-show. But that is an answer for another question.

