It's a charity, how is giving them an advantage over chains that put their profits into the pockets of billionaires a bad thing?
Funny enough an acquaintance used to volunteer at one and his main income (aside from the dole) was finding the good stuff, taking it, and selling it on ebay (he was delighted when someone's old school Game Boy with original pokemon cartridges came in one day...).
There is a loss to customers because instead of knowledgeable owners, charity shops are run by volunteers of varying quality.
I know of one case (through a volunteer at a charity shop) in which someone threw out a book of 19th century prints because they "threw out all the old rubbish". That would not happen in a commercial shop. I think its less likely to happen now that there are charity bookshops that tend to take the more valuable books, but I would not say it never happens.
Most importantly, the ability to avoid paying rates reduces the incentive to let the shops out, reducing supply and raising rents. IN many cases owners would rather have empty premises than let at lower rents and removing a cost of doing so makes this more attractive. The higher rents this causes that give chains such a big advantage over the small businesses they have largely replaced.