A review of Glasgow's parades policy, still the only one operated by a Scottish local authority, has made the recommendation after enforced changes to routes and times to several marches to avoid clashes with drinkers.
A number of parades in the city have also been amended to avoid coinciding with Rangers and Celtic matches.
Glasgow City Council has also resisted pressure to relax the ban on playing music while within 100 metres of a place of worship, even when it is not in use.
However, police commanders have the discretion to allow bands to keep a single drum beat for time keeping.
Meanwhile, protests over global politics and the cost of living have led to a recent rise in marches in the city, following a sharp decline since 2009.
Issue-based demonstrations such as protests against the so-called bedroom tax and wider welfare reforms have been the main catalysts for the increase, amid a continuing drop in events by more traditional parading organisations.
Glasgow introduced its policy on parades four years ago, with a view to reducing the impact on businesses and communities by attaching restrictions and moving to cut the overall number, once said to be bigger than in Northern Ireland's two main cities combined.
The policy is reviewed every two years, with draft recommendations put out to public consultation.
The latest proposals will be the first policy on parades to which Scotland's new national police force will be asked to contribute.
Recent high-profile instances have seen parades steered away from the Gallowgate in the east end and Govan areas.
The proposals state: "In terms of the playing of music, further restrictions may be required after considering the type of premises on the proposed route such as residential developments, places of worship, football grounds and public houses.
"All processions will be required to cease playing music when approaching and passing places of worship ... irrespective of whether or not a service is in progress, as instructed by the police.
"The council will maintain the current position that no music shall be played within a zone 100 metres either side of a place of worship."
Figures in the review of the past two years have found a reduction in the volume of around 21.5% over the past five years, with changes to how parades are registered bringing the number down further still.
However, while the figures are broadly evening out there has been a notable rise in non-Loyalist and Republican events.
A spokesman said: "The largest decline in numbers has been among the traditional marching organisations - loyal orders and republicans' groups.
"However, there has not been a similar reduction from other parade organisers, with annual numbers ranging between around 90 and 120.
"They include Boys' Brigade, trade unions, churches, community galas, charity walks and military parades.
"In recent years, there have also been a significant number of additional parades to campaign on political issues, from the bedroom tax and Trident to welfare reform."
Cllr Phil Braat, who is heading the review, said: "These new proposals are about fine-tuning that policy, which is still by some distance still the most substantial code for processions anywhere in Scotland."