It's much easier to cancel grassroots football because the consequences from the FA's perspective will be incredibly low-risk. But imagine telling Liverpool they haven't won their first title in 30 years, or that Man Utd haven't qualified for the Champions League or that Leeds have to miss out on £100m of Premier League TV money. The financial and legal ramifications would be significant.
They'll wait as long as they can, and don't forget we're still only in March. If they have to cram nine matchdays into June and July, for example, then that shouldn't be too logistically difficult. Next season would have to start later, but who cares about next season; a ball hasn't yet been kicked in that campaign. Binning all cup competitions in 2020-21 should enable leagues to squeeze a regular season into Sept-May - allowing for a pre-season (contract renewals, transfer window, pitch relaying, kit releases, season ticket renewals etc) of August-early Sept.
Obviously if the current restrictions are still in place by late June (which matches up with the government's 12-week 'turning the tide' period), then the null-and-void card may have to be played, but we're still way off that stage.
Edit: As the post above mine has illustrated, if South Shields are considering legal action then just imagine Liverpool, Man Utd, Leeds, West Brom, Portsmouth, Coventry etc getting their lawyers involved. It would be total carnage and could take the FA under.