Triads are important in any genre because they are fundamental. They are key to how most music is composed (generally speaking "harmonized in thirds"). And inversions are important, regardless of how the music is harmonized, in order to smoothly switch between chords.
You're talking about the blues. So let's pick any key and think about the progression. In E, a guitaristic key, we've got E7, A7, and B7. Forgetting about the 7ths, those are three triads alone: E, A, and B (major).
But, say we were talking about jazz instead. A common progression in jazz is a ii-V-I. So in the key of C we've got Dm7, G7 and Cmaj7. Those can be reduced to Dm, G, and C triads.
The point is, the vast majority of music can be reduced to a progression of triads. So knowing those triads is fundamentally important. Knowing them allows you to combine them (to form progressions) and build upon them (to form more complicated chords). And this doesn't just have to be chordally. You can play these triads as arpeggios for a solo as well.
Why inversions? Because, simply put, smaller intervals sound less dramatic. Let's back up a second. The point of inversions is typically for the sake of "voice leading" which is the concept of moving from one chord to another while paying attention to where each individual note (voice) of the chord moves to in the next chord. And usually you want each note (voice) to move as little as possible. Again this is because smaller interval jumps sound less dramatic. And in the context of switching from one chord to another, the less dramatic you can make those switches, the smoother that change will sound. There are exceptions. Sometimes you might want a dramatic, non-smooth, change. But that's an exception and up to taste.
Putting those two concepts together: you can spell out a progression either through harmony (chords, double-stops) or melody (ex. soloing) while making it sound as smoothly as you want it.
As a practical example: try putting on a blues backing track and limiting yourself to 3 strings. As a side note, this is a nice exercise to think of the guitar in string sets (1/2/3, 2/3/4, 3/4/5, 4/5/6) where you're only dealing with a single octave in a single position. So say you can only play the top three strings a single position. Now … you have to the play triad arpeggios of each chord (say E, A, B). Given that limitation, you start to see why inversions are important. You can't play those triads, let alone 7th chords, without either changing positions or shifting the order of the notes.
If you try both you'll probably find that, chordally, you can create smoother sounding progressions using inversions to minimize movement. And, melodically, you'll probably find the same thing and more freedom in that it allows you more smoothly connect from one note the next. You can still use larger interval jumps if you want to, but you aren't bound to them simply because the underlying chord is jumping a 4th. You can instead jump to the closest note in the next chord. That's voice leading. And that's why inversions are important.