The recommendations, which include potentially 100-plus local councils raising most of their finances, have been broadly welcomed across the political spectrum, with the Scottish Government defending its record on local government.
However, opposition parties said the report's plans would "reverse the SNP's power grab" and claimed it as evidence the "centralisation agenda" was "out of touch".
Only the Tories raised concerns about the creation of more councils, claiming that while they agreed with increased localism they had reservations about additional costs and "needless administration".
The Commission on Strengthening Local Democracy, set up by Cosla, has recommended handing local government full local control of the whole range of property taxes including council tax, business rates, land and property transaction tax, and the freedom to band and set taxes in ways suitable to local circumstances.
Proposing a Nordic-like model, it claims Scotland would be "fairer, wealthier and healthier if local communities had control over the issues that matter to them".
Professor Richard Kerley, of Queen Margaret University, a leading expert on local government and Commission member, said: "We also have one of the lowest turnouts in local elections in Europe. That is the canary in the coalmine.
"The turnout for elections really tells us about the public view of the systems we have.
"It's open to the Scottish Government today to determine a basic law which says 'this is how we will organise local services and maximise local democracy'. It's do-able now and it's do-able on September 19 whether it's a Yes or No vote."
Willie Sullivan, director of campaign group the Electoral Reform Society, described the report as "one of the most interesting and exciting statements to emerge in recent times" on local governance, adding people had lost trust in local government as its powers have become diluted.
He added: "It would be difficult to overplay its importance."
Green MSP Alison Johnstone said: "The current system is unfair and unsustainable. Other European countries take proper local government for granted, and we should aspire to that. It's essential we push the issue up the agenda whatever the result of the referendum."
Scottish LibDems leader Willie Rennie, who gave evidence to the Commission, said a number of the party's plans to strengthen local communities had been carried forward in the report.
But he added: "This new contribution reflects the chorus of people in Scotland who feel that the SNP's centralisation agenda is out of touch."
Labour's local government spokeswoman Sarah Boyack said: "There's a lot in this report that chimes with our plans to devolve more powers to local councils and reverse the SNP's power grab."
A Scottish Government spokesman said: "We believe local government will be an integral and essential element of an independent Scotland, and independence offers the opportunity to guarantee the status of local government in a written constitution, and to renew democracy at all levels of government.
"In setting up the Commission, Cosla confirmed the appetite that exists within Scotland for democratic renewal and increased local decision making."