First before I say anything, I've just had knee surgery to correct a
problem with my knee that's prevented me from cycling for about 10
years and I'm only on the newsgroup because my wife's about to buy a
Streetmachine. Now that I've admitted to having no credentials at all
about frame building, discussions on this this newsgroup seem to imply
that the frame performance is mostly based on stiffness. Once the
frame is strong enough to deal with the abuse life throws at it, a
stronger frame is unimportant. The stiffer a frame gets the more
cycler power can be applied more efficiently (I realize that there was
a discussion about having too stiff a frame).

If I'm correct about that, frame stiffness is again a function of
modulus and does not include tensile strength at all. All steels from
1020 plain carbon steel to the special through harndening tool steels
have close enough moduli that you day to day variation in cycling will
swamp the small change in cycling performance. Tensile strength is
only important when that cyclist hits a bump/curb/car/etc and it's
time to decide how badly the bike gets bent.

Second question, titanium and aluminum are rarely selected because of
their strength to weight ratios. They tend to be cited for their
excellent stiffness to weight ratios. If you are not constrained in
tube thickness, titanium or aluminum alloys can match the stiffness of
a steel bike with a fraction of the weight. The also tend to have
tend to have shorter fatigue lives and fun corrosion modes (if it's
fun for the metallurgist, it's not fun for the user). Saying that a
steel has the same strength to weight ratio as titanium is nice, but I
still think that stiffness(modulus) is the driving property and there
isn't a steel in existence that matches aluminum or titanium in
modulus to weight ratio.

I'm probably not going to change anyone's mind, but I'll give the
official metallurgy party line: Don't weld heat treatable steels
without giving them a post-weld heat treatment or understanding the
loss of strength caused by welding. The base metal isn't simply
annealed. The base metal has melted next to the weld joint (melting
the base metal is the definition of welding rather than brazing).
That metal has now converted to martensite; really strong and really
brittle. The base metal that didn't melt but is next to the weld is
fully annealed and likely to be dead soft for the base metal. The
area that didn't get fully annealed is over-tempered and much weaker
then it should be, and so on out from the weld until you reach
unaffected base metal. There are ways to get a mechanically
reinforced joint so this doesn't matter, but welding on a heat treated
steels is generally a bad idea.