Most definitely agree, Joker. You should be practicing all of it. And not just finesse with the right foot, but with the left as well. Even if you don't have 2 pedals.
I'm working on a solid 8th and 16th note beats with my right foot where I can sound like I'm keeping a solid double bass drum line but actually only doing it with one foot. This allows me to free up my left for some HH work.
A good exercise for left foot control on the hats:
Think about a basic jazz beat on the hats.
p = left foot step (closed)
x = blank note
o = left foot step (sustain)
I'll put the triplet groupings in parenthesis...
so a triplet would be:
(p-p-p) (p-p-p)
or with double bass pedals...
(r-l-r) (l-r-l)
so then a basic jazz beat on the hats with just the left foot...
(p-x-p) (p-x-p)
Now the trick is to make the first step on every soconde triplet an open hat note that sustains for the entire second triplet...
(p-x-p) (o-x-x)
Practice that with just your left foot. This then allows you to free up an entire hand since you would usually use your right hand to strike the hats.
Then get your right foot doing triplets and doubles and you can sound like you have 2 extra limbs since you have a complete rythym going with just your feet. Then add in your hands doing whatever your brain will let you do

Perhaps to start working the left foot in being able to do it's own hi-hat sustains, just work in single 1/4 notes.
p - p - p - p
Then, start controlling the open hat step. You basically step quickly and release to cause your hats to ring and stay open.
Sustain on the 1st and 3rd notes, while closing the open hat strike on the 2nd and 4th.
o - p - o - p
That make sense? I'm sure I'm not using the proper terminology but I hope you can follow my kindergarten attempts at writing out some patterns

If your left foot is good at doubles this should be pretty easy. If your left foot isn't, this is a good exercise to develop it without having to use double bass drum pedals.