The large majority of dogs benefit hugely from off-lead walks, and pose no threat to anybody they might encounter. They are usually much more interested in following their noses, investigating interesting smells, chasing squirrels etc. A dog that is prevented from following its natural instincts to run, explore, investigate by being kept on the lead all the time is likely to be bored, understimulated and display unwanted behaviour such as damaging furniture or becoming aggressive.
I think a better idea would be to allow dogs to be off lead (with the same caveats that apply now re being under control) at certain times of day - for example before 8am, after 6pm and between 1200 and 2pm. All dogs (except working sheepdogs etc) would have to be on lead outside those times. Dogs could get still get the off-lead exercise they require, but anybody who wanted to be sure they would not encounter an off-lead dog during their bike ride etc, could time it accordingly. It would be a compromise between the needs of people who would rather avoid dogs and those of dog owners.