Updated Answer
It is possible that a vote-siphoning tactic could be an effective one. You're not crazy or misguided here. Your cost estimates are about right, and actually siphoning off 1-2% of voters in a battleground state would absolutely have an election-swinging impact. However, the costs and risks associated with it are certainly enough to scare off any organization that hasn't gone off the deep end in desperation. The following, however, are reasons why it might not be so effective as it seems.
Something I should have previously addressed is that the effectiveness of 'siphoning' votes through a third candidate isn't as cut and dry as it seems.
From this NYT article, which discusses some of the math behind Ralph Nader's candidacy and the 2000 election vote share:
Among Nader voters, 45 percent said they would have voted for Mr. Gore, 27 percent said they would have voted for Mr. Bush, and the rest said they would not have voted.
Supporting a candidate who is more ideologically extreme than your opponent does not purely take away votes from your opponent. This dilutes the theoretical effectiveness of a third-candidate vote-siphoning strategy.
Another of the major issues with this tactic, which I briefly touched on in my first answer, is backlash. Campaign tactics can have negative repercussions on those who employ them - an election mail study in Michigan once provoked such negative backlash the researchers involved had to change their address due to the influx of angry mail they received.
Party organizations (RNC, DCCC, etc.) occupy a higher and more visible space in the political organizing hierarchy than smaller campaigns. A party organization caught doing something unsavory, such as mobilizing "the crazies" (as Sen. McCain might call them) on the other side by supporting an extremist candidate, could experience backlash effects which would have a negative impact on the entire party's prospects for the election. Major election scandals also tend to linger, like a dark cloud, for years or decades (ever heard of the Watergate Hotel?).
Your assessment of the resources needed for this tactic to flourish seems about right--Gary Johnson's campaign ran an ineffective and inconsequential campaign with $2.5M in 2012. $50M might be enough for a third-candidate to start taking in significant vote totals.
Although presidential campaigns are now run on massive budgets (>$1 Billion each between super-PACs, party organizations, and actual campaigns), $50M is still a lot of money to spend—especially on a largely unproven tactic. Parties and campaigns spend all the money they can afford each election: both the Obama and Romney campaigns in 2012 ended up with less than $13M on hand at the end of the election. Few campaigns or organizations would have interest in taking that kind of risk.
And it's all positive issue ads -- no negative ads, no consulting fees, etc. If you focus on, say, 3 battleground states, that gives you 25% of the visibility of a major party candidate. that should be enough to risk the 100-200k voters that are the margin in those states.
Positive advertising is not necessarily insulated from backlash effects. If it seems like you are "gaming the system" to one person, it will seem that way to many others.
There are also definite start-up costs associated with this tactic. You are suggesting fabricating a separate campaign from the one the campaign is already running. This means developing new messaging, recruiting new volunteers, and focusing on an entirely different population of prospective voters. That means new consulting fees, designer costs, media buy strategies, etc.
I've shared a few articles to get you started; there are more, but I'm not going to do all of your research for you. Much of my explanation however also comes from my academic and professional experience in campaign science & consulting.
Original Answer
Campaigns do in fact sometimes support 'extreme' and 'insurgent' candidates from the opposition. This is almost always a ploy to set up an easier general election battle by pushing a weaker candidate through the opponent's primary system. Here is one example of this tactic in use from the 2012 Senate election in Missouri.
This happens rarely for three reasons. First, campaigns have limited money at their disposal, and cannot afford to support a second insurgent candidate on their own. There has to exist an already close primary battle for the opposition party to decide it is worth funding the weaker opponent.
Second, parties control their own primaries across most of the US. This lets them set the requirements for even being on the ballot, creating a steep barrier-of-entry for all but the most serious and supported candidates. Without support from the party establishment, most candidates have no way of mounting an effective campaign.
The third reason this phenomenon is rare: it risks damaging a campaign's image while costing them money to do so. Presidential campaigns avoid it specifically for this reason. Plus, many insurgent candidates end up on the ballot anyway. See the 2000 presidential election for reference.
