I do not oppose it on moral grounds, but it cannot safely be executed by someone who is not at least moderately familiar with air travel mechanics, and people who are sufficiently familiar generally already know about it. So offering it as a "great tip" without mentioning that there are risks is a really hazardous thing to do.
EDIT: I would say that my opposition to it (for my own use) is based on the perceived risk/reward ratio being terrible. For someone who doesn't have a lot of money, and doesn't mind doing a lot of reading to carefully understand the risks, OR doesn't mind occasionally getting hit with serious downsides (like losing your luggage for an extended time), I think it can be a great strategy. But the risks on the downside are both significant and unexpected if you aren't warned about them. (Cancellation of connecting flights or temporary loss of luggage are very significant downsides if they happen to you without warning.)
I was going to wait to post this for reasons, but realized that was pretty dumb when the difference of a few weeks could literally save people hundreds, if not thousands of collective dollars.
If you fly regularly (or at all), you may already know about this method of saving money. The method is quite simple: instead of buying a round-trip ticket from the airline or reseller, you hunt down much cheaper one-way flights with layovers at your destination and/or your point of origin. Skiplagged is a service that will do this automatically for you, and has been in the news recently because the creator was sued by United Airlines and Orbitz. While Skiplagged will allow you to click-through to purchase the one-way ticket to your destination, they have broken or disabled the functionality of the redirect to the one-way ticket back (possibly in order to raise more funds for their legal defense). However, finding the return flight manually is fairly easy as the provide all the information to filter for it on other websites (time, airline, etc). I personally have benefited from this - I am flying to Texas from Southern California soon, and instead of a round-trip ticket which would cost me about $450, I spent ~$180 on two one-way tickets (with the return flight being the "layover" at my point-of-origin). These are, perhaps, larger than usual savings; I think 20-25% is more common, but even then it's a fairly significant amount of money.
Relevant warnings by gwillen:
Additionally, you should do all of your airline/hotel/etc shopping using whatever private browsing mode your web browser has. This will often let you purchase the exact same product for a cheaper price.
That is all.