I simply do not understand keeping and using lenses that are not sharp, have distortion, etc. I would throw in a box and forget. Then use only your lenses that are sharp and produce quality. Also, then save your pennies until you can buy quality lenses of the other focal lengths you want.
With the advances in technology and optics, your last premise is debatable these days.
The lenses I mentioned that I have were all bought years ago when I was on a budget and new to DSLR's. The 18-55 was part of the kit for my original Digital Rebel. I bought the 55-200 shortly after. Soon after that, being naive, I thought I could essentially replace both those with the 28-200. I was wrong. But the reason why I still use it is because it's my "I only want to carry one lens and I'm shooting in an environment I've never shot in before and don't know what to expect" lens. If I'm in a situation where I'm not sure if I'm going to need a wide angle or telephoto, but only want to carry one lens and I'm not overly concerned in getting the absolute best possible image quality, I use that lens. With that being the case, no, I don't use it often, but I feel better knowing I'm not selling it for a loss and it wasn't a complete waste of money. Since I already have it, I use it. But it's not a lens I'm going to recommend to anyone.
For not-so-serious shooting, it's a decent lens, and mated to my XTi it's still 1000x better than any point-and-shoot. But if I could do it all over again, I would have skipped that lens entirely. Surely many people have bought a lens that they either regret buying, or became obsolete though other glass upgrades or setting their standards higher for quality as they evolve.
I do agree with you 100% about saving pennies and getting a purchase right the first time. It's much better in the long run to hold out for quality glass that you're not going to want to replace than it is to buy a "budget" lens that's only going to see use until a better lens can be purchased. Lenses that fall into that category can often sit unused or are sold for a loss, or delay someone longer from getting the lens they really want.
Actually, buying the 28-200 was what made me wake up and decide that I wasn't going to waste money on a lower quality lens again.
But at the same time, realistically, not everyone has - or ever will have - the budget to buy any lens they want.
Sure, my last comment is debatable. Keep in mind though that the "do it all" lens I was referring to was the Sigma 28-300 specifically mentioned by the OP. I find it hard to believe
that lens would be equal or better than two Canon lenses covering the same focal length. You're right to say that lens technology keeps advancing, and maybe one day this will be a non-issue, but it seems to me lenses that have such a massive focal length range come with their share of compromises.
This is just my opinion, FWIW, if anything....
EDIT: Excellent point by Overread.
