I took the most efficient items of each stat (BF Sword, Recurve Bow, Cloak of Agility), calculated their stat to gold ratio, plugged in the formula for raw damage (no ARP), and made a chart showing the most efficient purchase with each iteration of stats. The starting point was 50 AD, 0.6 AS, and 0% Crit assuming a 100% Crit modifier. I solved for the general case so that I didn't have to spend too much time on it and then memorized the key points of the results. You're welcome to do the math yourself; I personally wrote my own program to iterate the formula for me, and I can't find the program right now.
And even though a good case was presented for the 1% crit, I still prefer the law of averages. In most fights, if I get off about 7-8 autos, that still only gives me a ~7-8% chance of getting ONE crit; I'd have to fight about 12 times for that one crit to happen (assuming a sufficient sample size), and that means I'm technically less powerful for 11/12 fights in addition to having a smaller margin for error on last hits and lower ability damage.
I do remember playing as Trynd once and getting 4 crits in a row pre-6 to nearly instantly kill someone. In the over 2500 games I've played, that's only happened one time where I got such an undeserved kill that should have simply been harass.
EDIT: Now that I think about it, that crit string happened before Riot made Crit Chance more consistent. At the time, you could potentially get 4 crits in a row with only ~10% crit; today, it more or less functions as an addition that procs when it hits the threshhold. For example, if you have 22% crit, then you won't crit on attack 1 (0+22%), attack 2 (22+22%), attack 3 (44+22%), or attack 4 (66+22%), but you will crit on the fifth attack (88+22% - 100%), and the process repeats. With this in mind, and with more testing, it may be possible to manipulate the timing of the crit making your point valid. However, I'm not about to begin testing this.