As long as you've accounted for other important parameters (tire-to-chassis clearance, ground clearance, etc), tire height can be chosen to optimize your final drive ratio. It can also negatively impact your gearing if you choose a tire size without considering the impact it will have on gearing. So that might be something you'll want to consider.
Also, your wheel size will determine what range of tire sizes you can mount. You definitely don't want to mount tires that are too big or too small for the wheel. In general it's a pretty narrow range of tire sizes allowed for a particular wheel size. Within that range, the 'measuring rim' size, or 'design wheel' size, will be what's considered optimimum for that tire. It's also what measurements like tire height will be based on. If you mount a tire on a wheel that's a bit smaller or larger than the measuring rim size - but still within the acceptable range - it will change the aspect ratio of the mounted tire and therefore change, to a small extent, both the contact patch width & tire height.
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