You were fed some bad info as a wee lad. Bullseye is great stuff. I've used a lot and never seen any problems it caused.
As to why they are on the fast end of the powder burn rate scale I'd guess pressures have a lot to do with it. Most shotshells operate at a max of around 10,500 LUP. The .410 can reach about 12,000 LUP and uses the slowest of the shotgun powders.
Shotgun and handgun powders usually are very similar in burn rates and in fact many shotgun powders are also the more popular handgun powders such as Unique and the dot powders as well as both 700X and 800X.
Average shotgun velocity is around 1200-1300 fps with lead shot. That's also close to the max of most handguns other than a few of the larger magnums.
Well, yes, clearly the burn charts show that only Blue Dot (of the Dot powders) is slower than Unique and all are definitely "fast". IMR 4198 is considered a fast rifle powder and it's slower than 2400, what I'd consider a slow pistol powder.
As to Bullseye (in handguns), even if it's doesn't burn exceptionally hot, if it's got the same peak pressure as a slower powder, it's got to "beat" on the gun more as it's the same pressure in less time. Perhaps the reality is, it's not enough to worry about, but hard to tell since the charts I'm finding don't give any sort of indication of "how fast" one powder is compared to another, just a ranking.
Somehow I find it ironic that the fastest powders, those most likely to blow the gun with an overcharge, are used for the lowest velocity loads. Can't quite figure out why it should be that way. I realize the idea of a quick pop vrs. a long push, but still can't find a reason other than powder cost to even want to use the faster of two powders when selecting a powder?
Seems like it's trading barrel punishment for lower powder costs?