That works up to a point (and no system is the perfect answer without adapting the game to suit it), but that places heavy restrictions on the options you have in that context. No two actions could be very similar. I could imagine it working well for games where thats not a problem though...

You can ease those restrictions though, with the addition of modifiers. As long as you keep it accessible, and such that it does not feel like a combo, you can go from four to eight or even more forms of context.

Depending on your focus, you can go even further with the control scheme. Taking an average game controller, you have four face buttons, four shoulder buttons, and a D-pad with a 4-16 direction control setup. On top of that, you have both analog sticks with full motion, and a downward press, meaning that at the very limit of the average we are examining, you have 28 forms of input. At this point, you have a question, what are the primary input areas? If the game relies on using both analog sticks constantly, with a high level of twitch-reaction, you would not want to map those twitch-action commands to places that are hard to reach, such as the face buttons. But if it relies on only one analog, you suddenly have either the face buttons or the D-pad open for fast access. This is a key factor.

What question this places before you now, if you are going to have context commands with modifiers, is which part should have quicker access. If a shoulder button is a modifier, there is no question about access, while if a face button is a modifier, that suddenly changes the priority of the actions done with such said modifier. One could use the depressing of an analog stick for a modifier, with the command then mapped to the triggers. That would then give you the four triggers without the modifier, four more for each analog, and then if you wish, an additional set if both analogs are pressed at the same time. But then you have the issue of priorities, again. Excluding the idea of allowing the player to decide which modifier accesses which context set, it would take a great deal of trial and error to determine how to arrange the sets per-modifier.

Unless you wish to apply an additional level organization. If you used a left-to-right organizational scheme to the commands, ranging from whatever extremes you wish, you could then tie in your modifiers - left stick and right stick - to the same scheme. Pressing the left modifier would give you more in that range of commands, and same for the right. But this could only apply if you limited your situations to three (or four) sets of context.

For your first example, I would allow the player to arm either item as the primary item and fire it with X. If a secondary item is present, it could be fired with Y.

Usually, whatever was engaged first is primary. If the player ran into the burning building from another location where he was firing his gun, then the fire extinguisher should be the secondary item. If the player ran into a hostile burning building from a peaceful burning building, then the fire extinguisher would be the primary item.

This gun versus fire extinguisher problem seems like it would be a rare one. I would assign one specific button to all other unique context sensitive situations. - Bash door, pull rug, talk to person, etc.