Tony ceremony dates even in the best of years are set 9 or 10 months in advance. That won't be the case here, but they've already stated they want a ceremony to coincide with the re-opening of Broadway, and to celebrate that Broadway is back – not to promote openings that may be 3-to-6 months away. Surely Tony performances and/or pre-taping will be built into the schedule of all shows resuming rehearsals late this summer, rather than bringing everyone back months ahead of time just to do that. And even if producers wanted to do it in June, and even if the shows knew by then who will be in their casts come autumn, CBS is the other key partner here – TV schedules are set months in advance, and they're not going to want to compete with the Olympics (if they even happen).
For comparison's sake, way back last June, The Kennedy Center Awards were postponed from December 2020 to May 2021, with "a later air date on CBS". In January, 4 months ago (and 6 months ahead of time), that air date was solidified as Sunday, June 6th (usually right around the time of the Tonys).
Anyone who assumes the Tonys can be suddenly pulled together in 3 or 4 weeks just has no real conception of how any aspect of the business works.