Why use stronger less accurate Pokémon attacks?

Solution 1:

why do people use Fire Blast and related moves?

Well, this is heavily due to the style of battling. Whether someone likes to play a riskier battle, like I think there's a saying that goes like if 'the more you risk, the more you might gain' (and of course, the more you might lose).

Is that little bit of extra power really worth it?

Re the answer above. It depends on whether someone feels the extra power but trade off accuracy is better. Some people feel they have a lot of luck, and rarely see it miss, some people would make the Pokemon hold a Wide Lens in an attempt to restore some of the lost accuracy.

Overall, how likely is Fire Blast to one-shot something that Flamethrower would two-shot?

That one might be considered too broad. There are various sets (in terms of stat distribution), various Pokemon (typing, base stats, abilities, natures) and various conditions (weather, items, buffs/debuffs) to take into consideration. And 1HKO are not the only things to consider. Fire Blast could 2HKO a Pokemon where Flamethrower would require 3 hits, or 3 hits for Fire Blast against 4 for Flamethrower.

You might want to read this smogon article where parts are discussing about Fire Blast and Flamethrower. It's based on Gen IV data though, but still something you might find interesting.

For instance, let me quote those lines:

Both of the OU Fire-types, Heatran and Infernape, have huge Special Attack stats with which they use to fire off (pun intended) monstrously powerful STAB Fire Blasts. Heatran in particular can even 2HKO certain Pokemon that resist its Fire Blast (such as Salamence).

Even Pokemon that are resistant to Fire-type attacks can and will be 3HKOd by a STAB Fire Blast from the likes of Moltres, Blaziken, Houndoom, and Typhlosion.

Fire Blast: This is probably the most popular Fire-type attack in the game. Amazing power, with passable accuracy (better than Stone Edge, at least) makes this the bread and butter for any Fire-type's moveset, as well as Pokemon looking for Fire-type coverage.

Flamethrower: Here is the reliable alternative to the above option. However, you'd be surprised at how many OHKOs/2HKOs you miss out on when using this move (like Nasty Plot Infernape failing to OHKO Cresselia). However if you feel you can't afford a miss, like on a Pokemon such as Choice Scarf Heatran that may be holding your team together against threats like Swords Dance Lucario, this is an effective move.