Your demonstration asserts that a plus 1 increases the chance to hit from 90 to 95%. That's a specific situation that doesn't match the reality of the game.
An AC that you hit 55-60% of the time getting a plus 1 doesn't lead to hitting 5% more often. The +1 to damage depends on levels.
If that's what you got out of reading my post, I don't think throwing more math at you is going to turn the tide.
But, just for the edification of the broader reading audience.
Assume two level 1 fighters, both using a longsword with dueling style, against an enemy with AC 13.
Fighter A has Str 15 (+2), Fighter B has Str 16 (+3).
Fighter A longsword: +4 to hit, 1d8+4 damage (8.5 average, 8.73 average with crits)
Fighter B longsword: +5 to hit, 1d8+5 damage (9.5 average, 9.73 average with crits)
Against AC 13, Fighter A has a 60% hit chance (9 or higher on a d20).
Against AC 13, Fighter B has a 65% hit chance (8 or higher on a d20).
Fighter A average damage = 0.6 * 8.5 = 5.100
Fighter B average damage = 0.65 * 9.5 = 6.175
Ratio of Fighter B damage to Fighter A damage: 6.175/5.100 = 1.211, or a 21.1% damage increase from the +1 bonus to the Strength modifier.