My 1997 Camry LE 4-cyl auto with 90,000 miles has started making a
faint noise in the front left hand side. The noise started at around
70K (at around the time I changed from the original Bridgestone types
to Michelins) and is slowly getting worse.

The noise is of a GRRR-GRRR-GRRR type, and is most easily heard when
doing over 70mph on a smooth road. Noise is not noticeable at low
speeds or on rough tarmac. It could be described as a hum, or a faint
grinding sound, but it has the slight lilt to it, as described. Not a
RRRRRRRRRRR sound, but a definite periodicity to it, as in
GRRR-GRRR-GRRR. I took the mechanic for a drive when it first started
up about a year ago, and he said he couldn't hear it, or that maybe it
was the tires, but now even my wife can hear it in the passenger seat.

The noise continues unchanged when I shift the car into neutral while
travelling at speed, which eliminates the drivetrain, I guess. The
noise slows as the vehicle slows.

I suspect a bearing problem, but I'd be interested to hear the experts
comments on what this might be.

I could see cupping making noises like that.

Hmmmm. What would you say to me if I told you this story?

Perhaps the tires cupped from hard braking, bad alignment, poor balance, or
combination thereof.

My 1997 is sprung loosely in the rear also. I believe it is the design.

Yes. They would like your money just as much as the buddy across the
street.

I believe the TSB is for the strut housings. Some rubber bushing that dries
out and makes noise. It will cost less to have that fixed.

Tires should be rotated about every 5,000 not 10,000 for best life.

No idea how many miles your old ones had on them, tell us.
The ones on there are ruined so you gotta replace them.
Get a 4 wheel alignment from the same shop you get the
tires from so there can be no finger pointing if they cup again.

I have 165,000 on my 97 Camry original struts. Some tires do cup
especially Dunlops on their own!

Problem is not with the struts but the strut towers bushing.