The main reason why second price auctions are so 'famous' is its simplicity. By simplicity I mean that to predict behavior (bidding) in this class of auctions is relatively easy. The revenue equivalence theorem is another reason, since under some assumptions (mainly bidders' risk neutrality), the auctioneer expects the same revenue with a 2dn price auction or 1st price one (in fact, any auction whose rules assign the item to the bidder with the highest valuation and leaves a zero payoff to the bidder with the lowest. You should keep in mind that the comparison is made in ex-ante rather than ex-post terms.
Coming to your particular example, you may not be able to get $15. Suppose that instead of running a 2nd price auction, you run a 1st price (i.e., you pay what you bid in case you win). As a bidder, you have to choose your bid without knowing what bids your competitors submit. Suppose you are the bidder with the highest valuation. If you bid 15 and you expect everybody else to bid their valuations, then you expect a payoff of zero since you win but you pay your valuation. Thus, you incentives to bid a little bit lower than 15 (say 14) because you would still win the auction (everybody else is supposed to bid her valuation), but now you get a strictly positive payoff (1=15-14). But this implies that you cannot have an equilibrium in which everybody is truthful (i.e., bids her true valuation), which means that you as an auctioneer should expect a price that is never equal to 15. This is due to the trade off faced by bidders between a higher probability of winning and a lower payoff conditional on winning. Given this, the revenue equivalence theorem ensures that in expected terms, you as an auctioneer can do as well using a 2nd as using a 1st price auction, with the advantage that the 2nd price auction is much more easy to analyze form a strategic point of view.