I hadn't ruled out anything. I had thought mortars, but there's a lot of infantry support weapons out there and I am not an expert. I wanted to see if there was an alternative I was overlooking it.
For instance, someone said grenade launchers, I hadn't really given much thought to that for some reason and I probably should.
I really wasn't thinking arty or field guns (Someone mentioned arty cannons, to be honest I hadn't thought of arty cannons at all, maybe I should look into that more, good tip). Thinking front line infantry here, probably mechanized dropped off by an IFV or Karnov, supporting a push in rough or urban terrain, (and to answer that third question) preferably overrunning static defenses, armor with few/no good anti-infantry weapons and lesser quality infantry or even support troops like combat engineers or enemy field artillery.
That's on the offense.
I put area denial in there because none of the other units I tend to pick (e.g. model mechs, vees) focus on that at all, and I realized I had ignored that particular tool in the toolbox, but I am unlikely to change my 'mech/vee preferences. So I thought that could be a role/function I could slot my infantry into. I've definitely used infantry to secure/hold/defend an important choke point before. On defense that's the most common thing I do with them. But I felt like adding an extra dose of area denial capability could be extremely helpful, especially in defensive scenarios.