Rather than try to address all of the incorrect notions regarding the advantages of timing belts vs. timing chains, I thought I'd start fresh and leave out all of the cross-posting.
Engine designers use timing belts for ease of implementation. Yes, that is engineer-ese for lowering cost. Timing belts do not require lubrication like a timing chain does so there is no need for hydraulic tensioners and lubrication. Timing belts are also usually slightly quieter than timing chains, although most people, including me, would be hard-pressed to tell what is under the timing cover just by listening to the engine run.
There is no conspiracy on the part of automakers to use timing belts as a ploy to make money selling parts. The profit to the automaker from the sale of a timing belt is not significant enough to make a big difference in the bottom line (at least for Toyota). Dealer and independent service departments make a larger profit from timing belt replacements than automakers because the majority of the cost of timing belt replacement is usually labor, which is supplied by the shop. The automakers do not get a cut of service department labor.
Timing belts do stretch slightly, but not enough to cause so-called "timing drift." The tensioner takes the slop out of the belt, and the crankshaft and camshaft(s) are driven by the toothed side of the belt. The belt does not grow extra teeth as it stretches, and the belt stretches evenly along its circumference. As the crankshaft pulley rotates, it moves twice as many teeth on the belt as the camshaft pulley regardless of the length of the belt.
Automakers generally specify a replacement interval for timing belts, and when adhered to, the incidence of a timing belt breaking prematurely is generally no greater than the incidence of timing chains breaking. As mileage goes over 200,000 or so miles, the likelihood of a timing belt that has been replaced at the specified mileage intervals breaking is lower than the likelihood of a timing chain breaking.
Engines that use timing chains generally have some means to lubricate the timing chain and so they tend to be a little more complex than one that uses a timing belt. Chains do not stretch but they do wear over time. Like a timing belt, any slop that develops over time is taken up by the tensioner, and since they are also driven by teeth, the ratio of links passed by the crankshaft sprocket remains the same relative to the camshaft sprocket(s) and so timing does not change. Timing chains in Toyotas will generally last the life of the engine. Even in the 20 R engines, it was the timing chain tensioner, not the chain itself, that failed first.