This is incomplete. Negative advertising a) motivates the already-motivated, but more importantly it demotivates the less motivated.
Essentially, your goal as the Democrat is to make the Republican moderate say "a pox on both their houses!"
And yes, it's more complicated than a simple straight line and a fifty-fifty split. We're talking about median positions floating in hyperdimensional issue spaces (the most interesting times in politics are the catastrophic jumps from one local minima to another). But the simplified model has surprising explanatory power.
Edit:
I didn't properly address your argument which, if I read it correctly, is that perfectly symmetrical strategies will cancel out in a perfectly symmetrical race.
That's true, as far as it goes. But the implementation varies, the candidates vary, the electorates vary (especially in the USA where you have gerrymandering -- over here electorates are carved out by an independent commission).
Nevertheless, the beauty-and-bile strategy fits the circumstances better than beauty or bile by itself. It's a minimum viable strategy.
The Republicans have a stronger 'base' that is more likely to turn out, while Democrats traditionally capture more undecided voters, but have a smaller base.
What this means is that in elections with lower overall turnout (Non-presidential year house races, for example) tend to favor Republicans, and their game-theoretic response is to generally 'Go after the Base' and swing more conservative (E.g. Reagan, Bush II, adding Palin to the McCain ticket, and the US House races in 2010 and 1994).
Democrats tend to have much more impetus to 'get out the vote' and get undecided voters to show up to the polls, even if they risk adding Republicans to the ranks, so you tend to comparatively more centrist Democrat Candidates (Clinton, Kerry, Obama). They also tend to do better nationally in Presidential Election years with high turnout (Ceteris Paribus).
If you have any interest in how this plays out in the actual nuts & bolts of voter targeting, Hal Malchow's "Political Targeting" (2nd Ed) is the Bible for beginners.
http://www.amazon.com/Political-Targeting-Second-Hal-Malchow...
This suggests that each race may have a seperate Nash equilibriam based on the canidates and the electrate.
Are there many "swing seats"/"marginals" in US politics, or does gerrymandering pretty much rule that out?