We clearly need an engineering solution to analyse this problem. I propose that we design a wobble-ometer to attach to the toe-end of saws in use. In order to do this, we need some funding, so we could apply for a research grant, asking for funds to analyse handsaw toe-end wobble with special reference to it's effect on climate change and it's contribution to world peace (because we could do with a bit of that round here) - we'd be bound to get extra cash if we phrase it that way. Then we could investigate the vibration of saws, maybe using different forms of damping to see whether tensioning was as effective as (say) putting a bucket of water under the toe-end of the saw, or sticking a lump of chewing-gum to the toe-end of the saw to stop it flapping around. Once the research information had been collated, the design and development programme for the wobble-ometer could go ahead, and manufacture arranged. With luck, the whole lot could be done to allow a release to market on 1st April 2017, allowing hand-tool users to check their saws for toe-end wobble.
Alternatively, we could do as Mignal suggested earlier; wait until Rob Streeper (or somebody else) has done a bit more work, then pass two otherwise identical saws, one tensioned and one not, to a few competent woodworkers and ask, "What do you reckon to these, chaps?"