I don't have an H-shifter, but
@MikeGrove could comment on the use of shifters and eliminating shifter lag. Maybe
@SAMHAIN85 and
@Neutty could also chime in.
As far as I understand it, and again this was only explained to me - and it's rather confusing.
Let's say the car you're driving has extreme shift lag between 2nd and 3rd - and you are very commonly shifting up from 2nd to 3rd. You can leave the H-shifter in 3rd position, use the paddles and auto shift for everything else, but when you are in 2nd and want to go to 3rd you need only slam the clutch and the car will go into 3rd with little to no shift lag. This eliminates the risk of missing your shift, or getting it stuck in neutral - and you can use the paddles for everything else.
Or maybe it was you can premove the H-shifter into the gear you want, then just slam the clutch and it'll shift, basically instantly with no lag.
I don't have a shifter so I can't comment.
All of that being said, shifter users accelerate out of corners much faster than non-shifter users, so there is a drastic shift lag reduction. This is regardless of how you use the shifter (how it was meant) or in the somewhat exploitative way that was explained to me (which I tried to explain above)
Here is a good example.
Look at SRC starting from pole - the initial launch from SRC is good, but it's the secondary launch that is insane - that's the advantage the shifter has. Sometimes the advantage is just the start, sometimes it's at the start and it's accelerating out of corners during the race.
Our most recent endurance race is a good example, Neutty and Sam were doing mid to low 2:16's - my very best lap was a 2:17.5, some of that speed difference could be they were just better - but imo at least half a second of that time is the lack of shift lag (basically I stay in 3rd through the whole track and avoid shifting as much as possible because the lag from 2nd to 3rd is so bad).