Why would this be desirable? If you grip tightly with a sweaty hand you can be on the nib in no time and if you grip lightly it just slides slowly which affects the size of your writing. Straight would be better but it's still going to slide unless you grip hard... I must be missing something when it's so common but I'm trying to start afresh questioning everything and my inky finger says it's not good.
It is desirable (evidently arguable) because a taper accommodates for people with different preferences with respect to section girth; not everyone grips their pens at the same spot. For example, my fingers rest on where there usually are threads, and I prefer a longer section when it's available. I do write with pens varying designs though.
I must admit, the pens that you already have, i.e. the Parker Duofold and the Sailor 1911 are actually pretty good pens as they come. Getting a new pen is always nice, and in certain cases, a differently designed pen does make it easier to hold; i.e. you're gonna find a tapered, hooded nib pen like the L2K terrible. But the root of the issue is probably a problem with your fundamental technique.
Maybe share a few pictures of how you hold your pen?
Also, going through the lessons here might help:
https://palmermethod.com/Recommendations? Must be a fat pen, and if it were free that would be lovely ) The Visconti Homo Sapiens with it's alleged rubbery texture and hydroscopic properties sounds perfect especially as it has a little flare near the nib. Far from free though!
The Visconti Homo Sapiens is kinda overrated. YMMV. Thought about getting one several times, but always changed my mind after trying the pen in person. Several times across the last few years.