OP:
If I wanted to take time based plots, is that doable using reasonably priced tools, or is that a pro assessment job?
Room EQ Wizard (REW) has a variety of tools for that, and their forums are very helpful. Here’s a starter page.
Let me give you a little more background. For frequency response REW and similar tools (I use OmniMic) gate the signal above the bass. That is, they stop listening a few milliseconds after the impulse start to arrive. This deliberately excludes as much of the room as possible to get the response of the speaker. The sound waves are still busy traveling back and forth around the room for a much longer time period than this.
Our ear/brain mechanism does not hear like a microphone. We don’t stop listening, but integrate the experience of the direct sound and the reflections over time and this fully integrated perspective is what gives us an impression of the tonal balance. Often audiophiles only think this is an imaging problem but there is a very significant effect on the perceived tonal balance.
If you ever hear Fritz speakers at a show, he travels with only a few absorber panels. He knows what he's doing, and that his speakers will sound more full that way. We should all take a lesson.
In a very reflective room where the mid/treble bounces around for too long our hearing tends to exaggerate the mid and treble frequencies, so as a result will sound as if the speakers lack bass. So, a tip I often give which people resist is that adding mid-treble absorbers and diffusors will improve the apparent bass, and none of this is captured by simple frequency response plots.
The other thing these plots fail to capture is how having multiple direct reflections, and / or the absence of the right diffuse sound field ruins the illusion of an audio image.
In the bass things are different. The wavelengths are so long that it’s nearly impossible not to integrate the room, so as a result your frequency measurements are integrated. Speaker builders always face a challenge with this and use a variety of techniques to try to get the real speaker measurements like putting the mic 1/4" in front of the drivers, measuring outside, etc.
While room correction software may do a lot for the bass and maybe even correct for perceived extra mid/treble they cannot stop reflections. That’s why in my mind the two approaches are not equivalent but complementary.