Why are financials for public companies released quarterly? My guess is this started for practical reasons when updating balance sheets, income statements, and cash flow statements had to be calculated and audited by hand.
But these days, there's no technological limitation to giving shareholders more frequent updates. Now that transactions are being recorded digitally anyway, stock exchanges could demand real-time (or more realistically bi-weekly) public financial statements.
My main concern would be getting numbers audited so investors could be confident in their decisions. Instead of auditing statements continuously, I'd propose having auditors do random checks (like public transit ticket inspections). All companies would be checked at least quarterly. This way audits could continue to be in depth, without fear of time pressure altering the findings, and companies would always be incentivized to give an accurate representation of the economic reality.