There are several negative consequences, a few of which Socrates has stated.
First of all, the fact that you may lose a lawsuit does not necessarily mean that your case was frivolous or wrong-headed and punishing people for pursuing their legal rights in a close case by forcing them to pay the legal fees of the opponent, over which they have absolutely no control, is inequitable. Additionally, the development of the law requires people to pursue cases where the outcome is not set in stone.
Secondly, and most importantly, a loser pays rule benefits the deeper pocket (which really is the whole point of the loser pays movement). Adding the prospect of having to pay a defendant's high-priced attorney's fees in addition to the plaintiff's own attorneys fees should a plaintiff lose would discourage people without money from pursuing legitimate claims more so that exists currently. There are plenty of mechanisms currently in existence to deal with frivolous claims without punishing people with legitimate claims that happen to lose.