I can't find the exact quote, but Ernie Accorsi once discussed the Manning trade in a positive light - less first round picks mean more money to go after proven free agents.

That is kind of nutty. Draft picks can be signed for less money than what their market value would dictate if they were free agents (since the team that drafted them has monopsony power over them). Proven free agents, on the other hand, must be signed for exactly what their market value dictates since they are free agents.
On average, a $10 million draft pick will handily outperform a $10 million free agent. (See figures 9 and 10 in
this paper and note that all draft picks, on average, have positive "surplus value" -- i.e., they outperform veteran free agents, on average, per dollar of compensation paid to them.)
I thought the Loser's Curse was that bad teams waste money giving huge bonuses to unproven players who don't give them a good return on their money?
I think the "Loser's Curse" is a play on words, playing on the Winner's Curse. The Winner's Curse refers to the fact that winning bidders in an auction typically overpay based on the item's true value. (If an item is worth $15, a given group of 20 bidders may place values on it ranging from $10 to $20. It's the guy who values it at $20 who will win the item, and he will pay more than its true value for it. So the winner is actually a loser when it comes to value.)The paper is called the "Loser's Curse" in part because the draft is kind of like an auction, with various teams "bidding" on the top draft pick by offering to trade up. Whoever offers the most "wins" but is probably overpaying.
And it's also called the "Loser's Curse" because its principle finding is that low first-round draft picks are worth more than high first-round draft picks after taking salary into account.
So the best teams in the league, who go deep into the playoffs every year, end up with draft slots that are worth
more than those held by the losing teams. Although the draft is theoretically supposed to promote parity, it has the opposite effect. The worst teams get "worse" picks (in the sense of having less surplus value after taking salary into account) than the best teams do. So the losers are cursed in the draft in a self-perpetuating cycle of disadvantage.