Good wheels, like many other bike components, become important when you start to have that desire to ride centuries (100 miles) or longer distance. You would want to learn how to maximize your energy reserve. The less weight you have on you or on your bike, the less calories you’ll have to burn to cover the same distance.
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What does this have to do specifically with wheels you’re asking ?
Well, wheels have their own weight. And wheels will need to rotate in order for you to move forward. Guess who will provide the energy for wheels to rotate ? You ! Let’s take an example to illustrate my point. Take an empty plastic bag from your grocery store, and put a donut (light weight) in it. Now, with your hand start to swing your plastic bag in circle. Keep doing that for 100 revolutions. Now stop and replace the donut with with a pint of ice cream. Repeat the exercise 100 revolutions. You should normally sweat a little bit more with the second exercise. I think you get the point. Anything that you can see on a bike that makes rotative motion, you are the one who will provide the energy for that. It doesn’t matter much when you go for short rides. But when you sit on the bike for 5-7+ hours for your long distance ride, it will make a big difference.
Get the best wheels you can afford.