"as the old adage goes" is correct and usable in written English. This phrase is commonly used when someone wants to provide an old saying, proverb, or wise saying as a reference to support a point. For example, "As the old adage goes, 'A stitch in time saves nine' - it is better to act now and avoid future problems.".
As the old adage goes: writing is mostly rewriting.
As the old adage goes: nothing ventured, nothing gained.
As the old adage goes, there's no such thing as bad press.
Yet as the old adage goes: "Be careful what you wish for, because you just might get it".
Write what you know, the old adage goes.
Fighters fight, or so the old adage goes.
The more things can go wrong, the more things will go wrong, the old adage goes.
When I feel like I can't trust my brain 100%, Ludwig really comes in handy. It makes me translate and proofread faster and my output more reliable.
Claudia Letizia
Head Translator and Proofreader @ organictranslations.eu