It isn't a matter of controlling when it happens, it is an issue of what sort of impact it has over the long run. It would be like including archetypes and trying to estimate how much extra damage the assassinate feature could do. It simply isn't practical to include nova abilities, of which action surge is one. Something like action surge would double the expected damage for a single round, but how many rounds of combat are there? How much expected value can you place on it.
At best, you can try to estimate it, say on average 2 combats per short rest averaging 3 rounds each. Then, the boost in damage from action surge would be divided by 6 to spread it out over all rounds involved. In that case, the average damage boost to DPR would be about 2.65. But, if you decide maybe there are 4 combats per short rest averaging 5 rounds each. Now, action surge is used in only 1 round out of 20, brining its average boost to less than 0.80, in which case the Fighter would still average less than the Rogue.
As far as critical hits are concerned, they only add about 0.225 DRP for a Fighter since only the weapon dice is doubled, but for the Rogue it is a boost of 0.4 at level 1 and jumps up to 1.975 at level 20. So, with sneak attack critical hits are very important to the rogue.
Sure, fighters get there damage all the time, but 5E is a team-oriented game and the rogue in our group adds his sneak attack damage well over 90% of the time. The party recognizes his damage potential, including the battler-types in our group, and so we work together to try to get that sneak attack damage in every possible round. In a like fashion, our casters buff our fighter to keep him tanking, etc.
Finally, as to my "unilateral dump on" fighters, I love fighters and they are one of my top three classes to play in all editions of D&D as I wrote in post (#143). However I have always, in all editions, found them to be lacking compared to other battlers and we have always house-ruled them to make them the best at what they should be best at: damage with weapons.