Apart from casting distance...
If the line is too heavy for the rod then it could, in theory, damage the rod or the fish when pressure is exerted.
It is more visible in the water being (generally) thicker.
I use 15lb for pike, or rather I used to until I got braid, as it was more abrasion resistant if they got their teeth around it plus you're more likely to get your trace or lure back when they get snagged up. (I switched to braid for increased breaking strain versus diameter plus better bite indication for my piking).
I don't however profess to be a seasoned carp angler so I'm sure there will be a good reason for 15lb line now.
)
I personally don't use and wouldn't feel the need to use that for targeting 20lb average fish based on my angling experiences and the type of fishing I do.