If you think the rapier is too good, would you use this? What does it break? (DEX-clerics?) How can we improve it?
Here is the question: what problem are you trying to fix?
Is the problem one about certain builds (such as rapier/shield fighters)? Is it a problem with the weapon table balance? Is it a problem with finesse being a default build for certain "skirmisher" classes (rogue, monk, ranger)? Is it a problem with certain weapons being neglected in favor of finesse weapons?
Lets look at each separately.
First, the weapon table is hopelessly fubar. Seriously, heavy weapons begin and end with greatsword, tridents are martial spears, rapiers are king of finesse, and there is no reason to ever use a heavy crossbow since the only classes proficient in it gain extra attacks that make it a trap option. If you're going to try to fix the weapon table by changing finesse, you are only doing one of nearly a dozen fixes needed to balance that table.
Second, I have no problem with rogues, rangers, and monks using finesse weapons as the default fighting style. Rogues don't always get sneak attack, monks need it as the only way to get consistent damage, and rangers need all the help they can get dual-wielding. Either your are weakening all of these classes (by making them wait/pay for the damage boost) making them all MAD, or giving them a benefit that replicates what they get anyway, to which I ask what is the problem?
Third, the fighting style is basically a tax. You are basically giving a scaling dueling style + protection style for non-heavy armor. You've also killed dual-wielding stone dead as, barring a feat, you can only dual wield light weapons and all but one finesse weapon is light, meaning the two-weapon fighting becomes "using a greatsword, but requiring two to-hit rolls". Dual Wielding has it hard enough as is.
Finally, you're really only delaying the acquisition of dex-to-damage by a level (fighting style for ranger/paladin) or three (feat for non-vumans). Anyone serious about the style is going invest the resource in it anyway, and your back at square one around 5th level. If giving dex-weapons a 1-3 point damage penalty in tier 1 is big concern, then go for it. I barely think its worth the hassle.
So if you are going to change finesse, be prepared for a lot of options to become sub-optimal, dual wielding being the primary example.