Once again. They DO NOT do this anymore and haven't for probably 20 yrs, so this is not a concern. they do not have you put them on the floor. I and my DH have also flown a lot and have never seen a child hurt from turbulence.
The FAA brace position recommendation HAS changed, but it sure has not been twenty years since it was changed: the current recommendation came out in 2003:
"Children which are occupying approved child restraint devices should be
braced in accordance with the manufacturer's instructions. Children in
passenger seats should utilize the same brace position as adults. Adults
holding infants should provide as uniform support as possible to the infant's
head, neck, and body, and lean over the infant to minimize the possibility of
injury due to flailing."
The cite for this is FAA Advisory Circular AC121-24C (2003) -- This URL is really long; so you'll have to cut/paste it to go to the doc:
http://www.airweb.faa.gov/Regulatory...idance_Library
/rgAdvisoryCircular.nsf/1ab39b4ed563b08985256a35006d56af
/2026259a7a7247f986256d7a00508ba7/$FILE/AC121-24C.pdf
Naturally, the FAA doesn't illustrate what this position looks like in that document, but the CAA (Canada) does illustrate it in their documentation of the same standard:
http://www.tc.gc.ca/CivilAviation/c.../AC0155_att.htm
Turbulence injuries do happen, I've seen them several times; mostly just knots on the head or bruised legs from hitting the bottom of the overhead bins and then bouncing back down to hit the armrests or tray tables, but I have seen a few bloody noses and cut lips, too. In any case it is enough to insure that the rest of your flight is occupied with trying to soothe and comfort a screaming child. (The official count that the FAA keeps notes about 50 turbulence injuries a year of passengers in general, but that only counts people who need to go to the hospital for treatment; bumps, bruises and band-aid cuts don't get recorded.)
Personally I don't do lap-carrying, primarily because it's a PITA to try to keep a frantically squirming child or a dead-weight sleeping one on your lap for a few hours in such a confined space. If I had to pinpoint a cut-off age at which the discomfort of holding them solidly outweighs the added cost and hassle of carrying the seat, I'd put it at about 11 months, myself.