Muuuum, going to disagree a bit there with an explanation...
I have been shooting for 54 years and have shot MORE than a ton (literally several) of cast bullets and jacketed bullets out of PB rifles, pistols and revolvers and in my 'Magnumitus' phase was shooting those 3000 to 4000 FPS velocities (I had every Weatherby, Remington and Winchester Mag cartridge rifle ever made and usually ended up only keeping the action and rebarreled and restocked for long range shooting) at VERY long ranges of 1000, 1500 and even 2000 feet and I ABSOLUTELY can swear that the sweet spot for bullets is NOT 3K to 4K as currently constructed (even the mono-copper bullets). I also shot BPCR Big Bore for years using cast and paper patched bullets and got some of my best accuracy from them around 2K, better than many 'modern' centerfire cartridges ever dreamed of. I've shot NRA High Powered rifle, both rifle and pistol Silhouette, combat pistol, small bore benchrest, etc... shooting has been my life, all my life since my dad got me reloading at 10 years old
So the high speed is doable yes but it is a lot easier to get accuracy at UNDER 3K than over.
To shoot that much I had to reload (although I did buy factory ammo to compare too at times) and I learned to make any rifle much more accurate with tailored loads than factory ammo. Most rifles sweet spot in accuracy is not the max but usually was right around 90% of max by the way, no matter what power level of the cartridge. In Simi-automatic pistols and revolvers the same seems to hold true. I did a lot of load development using a Ransom rest which holds the hand gun, not the person, so as to take the human variation out of the equation and again, I learned that there is no 'best velocity' for any bullet but slower, IE whatever the cartridges max was, the most accurate was the 80 to 90% load(s)
Now I have left PB entirely and {for the challenge} only shoot PCPs which due to the physics barely reach supersonic and use a lot of air to get there and in my dozen of guns find again that a little slower is more accurate than the gun maxed out (and I have 4500 PSI [instead of the stock 3000 PSI] custom Texans in .457 and .357 that are a LOT more powerful than a stock rifle as just one example where it shoots a little better backed off a tad.)
So my take is that there is NO best velocity for BULLETS, but you can push them too fast FOR THAT PARTICULAR GUN TO SHOOT ACCURATELY. And in the lower regions of 750 to 1050 for subsonic and 1200 to 2600 for supersonic is easier to achieve accuracy in the total system of gun, cartridge and bullet.
In my 'slug dedicated, chokeless' air rifles (which I have come to love, strangely enough) slugs can do just as well in accuracy in the 'quality' rifle at 600 as at 1000, but I don't usually tune in the lower ranges because who wants to bother with the mortar trajectories the slower speeds give.