It would be merged in one general "attack" stat. This hypothetical stat would be equal to the current attack or sp. attack stat of existing pokemon, whichever is higher. Attacks still have the physical/special split, so the defense and special defense stats remain, but both physical and special attacks are based on the same attack stat.
Would this have any impact on the gameplay?
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Anything with a decent attack or sp. attack stat becomes an amazing mixed sweeper (provided the moves are there), and probably most of the existing mixed sweepers lose their value due to having a lower merged attack stat.
Then of course there's things like Huge Power, any attack buff now boosts both physical and special attacks, etc.
Even with my nooby analysis, it's obvious that this would have a big impact on gameplay.
We'd probably see a new wave of hyper offense unlike any other. Most walls will now be nearly useless since anything with enough attack to be considered a sweeper will be able to hit on both sides of the spectrum (for example, the ever-classic special sponge Blissey can't even wall a common special sweeper without a newfound fear of physical attacks). Essentially, every sweeper would be a mixed sweeper, and since attack is now a single stat, EVs wouldn't have to be spread between attack types (so most sweepers will just run 252 Attack/252 Speed, or something close to that).
So essentially, it makes walls become much less useful because the defenses are still split but every sweeper can ostensibly carry both types of move. Sweepers will no longer need to be varied by which side they hit, so only the Pokemon with the highest attack stat are likely to be used. This change homogenizes the metagame to an intense degree. It's even worse than recombining the Special stats would be, because at least if the special stats are recombined physical attacks would still have a purpose.
...God, Rampardos would become even more beastly, to the point where it might actually start seeing use. (Sheer Force Choice Scarf Rampardos with like Fire Blast/Thunderbolt/<Rock Move>/Focus Blast or something would rip through things.) It also gives a massive advantage to earlier-Gen Pokemon, given back then practically everything got Thunderbolt and Ice Beam, but in Gen 4 and 5 they cut down on it. There's also already-good Pokemon like Tyranitar, Dragonite, Alakazam, Gengar, and Keldeo that have 1 attacking stat massively higher than the other but a good movepool for the other stat that would potentially get broken. (It would be hard to believe something like Tyranitar or Gengar wouldn't become really, really powerful.)
It also makes Psyshock, Psystrike and Secret Sword more or less useless since nothing's then stopping you from just using a physical move. It also means Belly Drum is much more powerful, and would allow for mixed sets at massive power. ;p
Also, may I point out that defences remaining split makes ZERO sense with this.