Sure if it is horrible it might be necessary, if warm water and disinfectant spray don't sort it out. We have not had our grocery shopping leak that badly that I can remember.
It really depends on the supermarket. If they sell the expensive chicken that comes sealed in rigid plastic from the "manufacturer", it doesn't leak. But that's double the price. When you're buying the normal-priced chicken that the supermarket apportions out into those yellow styrofoam trays that they then seal in plastic themselves... ugh. Chicken juice everywhere.
I see, meat packaging is different in the UK. Styrofoam trays are not used in any major stores, they all use the same rigid sealed containers, even the cheap options.
Butchers cutting meat for you is much less common in store now, those that do have a butchers counter wrap it in a plastic bag which seals it pretty well. Small independent shops might do it differently.
I think in general those styrofoam trays are not used much because they can't be recycled. You still find them used by some takeaway food places though.