If we're being technical, shuffling actually lowers the house edge a bit if you are not counting cards, but completely restores the edge if you are trying to count cards. This happens because for each hand of blackjack it is more likely that the last card played is a high card (you are more likely to draw again on a low card), so the remaining deck is slightly lower on high cards on average if you don't shuffle compared to shuffle, and high cards are good for the player, so not shuffling is better against non-counters, but a lot worse against counters.
They most definitely have an edge on slot machines. The fact that there are at times local maxima that favours the gambler doesn't impact the overall edge. This is the same as lotteries with a carry-over jackpot etc. The jackpot is paid for by other gamblers who played against really bad edges, not the casino.