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.