I played (and I have been planning to play again) D&D using virtual tabletops, but even at lower levels (6ish) the combat seemed to become more of a pain because of its extreme slowness.

My main problem with it is the excessive number of attacks that will make the warrior with greater two weapon fighting and haste a true nightmare. So, I decided to reduce the number of attacks to something along these lines.

When the BAB reaches +6, the character doesn't gain an extra attack, but inflicts double damage (from weapon AND strength, as if two attacks landed).

When reaching +11, the character gains an extra attack at -10

When reaching +16, the character doesn't gain an extra attack but inflicts 3 times the normal damage (from weapon AND strength, as if three attacks landed)

I have only two problems with this:
Does this actually unbalance the game allowing the characters (especially fighters) to inflict much more damage than before? Technically, if both the level 16+ Fighter's attacks land, they will end up doing the damage of 6 attacks. To do the same amount of damage as per the previous progression, I should keep the 2 attacks at twice the damage, but what do I give fighters at lvl 16? A hug?

Also, how do I implement TWF in this without increasing the number of attacks? I was planning on adding the roll of the weapon die + 1/2 the Str modifier, non-multiplied for TWF feat. The damage would be multiplied by two for Improved (since it give the extra attack), and tripled for Greater TWF. All the attacks would be penalized by a certain amount (maybe just -2 with a light off-hand weapon).

My main goal is to allow everybody to feel useful (particularly fighters at higher levels), allow mobility (sometimes, a -10 for an extra attack is too much, so a simple standard action will be taken instead of a full-attack, allowing movement), and save time with combat.

Is this a viable alternative or not? I like homebrewing, but I don't have the chance to test this rule at the moment, so I don't know how effective or ineffective it is.