Worries about a gear ratio of 1:1?
1:1 and similar ratios are considered bad in automotive gearboxes. If there is one bad tooth it will soon take others with it, if it is always meshing with the same teeth. Automotive gearboxes tend to use coprime ratios (where the 2 gears have no common multiple) to avoid this.

There really isn't a similar issue on a bike. I suppose it might be a good idea to have a prime number of links on the chain to even out wear in case of a bad tooth, but the sprockets never come into direct contact, so that shouldn't be an issue.

Resonance shouldn't be an issue. the resonant frequency of the bike is going to be way higher than your pedalling frequency. It'll be in the audio range. Just give it a tap and you may hear it ring.