people keep missing the point though. we are talking about a standardised infantry weapon that is to be carried In Addition to the primary infantry weapon of the period, a flintlock musket. In my collection at home i own a 1834 Model 1822 Springfield Flintlock, still with its 18 inch Bayonet. Now this weapon weighs a lot, (About Double my Lithgow No1 MkIII* .303 and Husqvarna M38 at a guess) as well as being significantly longer (1.45 Metres).
Now Imagine a combat situation of the period. Closed ranks and the opposing lines approach for close combat. one line possesses Muskets tipped with bayonets, the other is equipped with muskets and the sword i think would be most effective in this role, a roman Gladius. Both lines would wish to fire for as long as possible the last volley being fired at extremely short range. the bayonet equipped side before charging/receiving a charge merely have to fix bayonets.
the gladii equipped troops would however have to sling their muskets (not to easy in tight ranks) and then draw their gladii. throughout the engagement the gladii equipped soldiers would then have to fight with a 5-8 kilo weight which is 5 foot long slung over their shoulder. also the gladii in roman periods was so deadly due to the mutual support of the cohort with the large shield covering each other. the gladii without the shield is only one half of the weapon and it would be ridiculous for troops of that period to carry shields. also the gladii would provide no defence against cavalry and the gladius equipped sodiers would be forced to push through the bayonet "Hedge" before engaging. and this would be a lot harder than merely swatting aside the bayonet of the man facing you and closing, because the men on either side of him also pose a large threat to ur wellbeing.