If we are talking about MTB 26" wheels, then putting really skinny tires on has one really bad downside. Your wheel diameter is reduced from the 26" design diameter of a normal tire down to about 24" with the 1" and 1.25" tires. This dops the gear ratios down a lot. If your bike has typical MTB gearing you'll run out of upper gears often then your tire width will have the opposite affect to helping you keep up with folks on road bikes.