The 18-55mm + 55-200mm is a lot cheaper than the 18-200mm while giving better IQ at lower build quality.
The 18-200mm is very convenient as a single lens, but if you have the money and time to switch lenses, the 17-55mm f2.8 + 70-200mm/80-200mm f2.8 is an amazing combination. If you don't want to spend so much, I would suggest the 18-55mm + 55-200mm/70-300mm.
Hit the nail right on the dot.
To add on, the reason for getting 2 lens to cover that range is due to IQ, at the cost of a higher budget as well as the hassle of changing the lenses.
For me, I have a 17-50 f2.8 tamron (with a 55-200 or 70-300 in future), which beats the 18-200 (if u're comparing only the equipment) but comes at a higher cost instead.