Interesting question, I had to read.
I’ve struggled with ‘giving a solution to a problem others don’t see’ in my work also. I half agree and half disagree and am now compelled to write my own take to you so bear with me. ;)
What you’re describing sounds like ‘telling them what they want to hear’. For some that works, and they call it a relationship. If I were your client, I’d see it as fake (sorry to be blunt) because if I am to consider it a relationship you have to have my interest in mind too. Secondly, I’d question your competence when the issue comes to light down the road and possibly blame my choice in working with you. Your method sounds to me (could be misreading it) like it works if you just want to secure your position with the client in that you remain in a favorable light. That being said, it will only work for you until they stumble across the issues in their process/work (probably inevitable they do stumble cause you wouldn’t pine over something non-critical I guess).
I agree the client relationship is important, and as a business you keep that above all else. So No, I would not convince them (belligerently or debate), indeed they want to keep to a process or standard it only adds an obstacle/stress so on. And they have to like you and feel you are reducing the burden, not a burden yourself. But you should mention it tactfully imho, the pros/cons of what you’re proposing and let them turn it down. The reason being when they stumble across it, they’ll remember you risked business to inform them and had their interest first. Further, they’ll remember you have a solution and come back to you.
Someone once suggested to me to prepare my solutions and wait until they see the problem to propose it. Or develop my influencing skills to tackle this. Alternately, you can offer your services at a later date (perhaps once they see the issue, or have resolved the barriers keeping them from addressing it now). Another option is to be so tactful they can’t ignore your point. So point out the problem first as a casual question…’what if…[happens]?’. Let them realize they don’t have a solution, or dig a plausible one up and start the dialogue with you from there. Giving you an opening to provide a solid solution immediately (Identify the problem — antagonize (or let them agaonize)-and then the solution). Maybe I’m stating the obvious and you tried these. I had a boss (business owner) who used to turn down clients if he saw they’d shoot themselves in the foot. He’d point out what they need to do and tell them ‘call me when that’s there, cause anything I do now would only fail you.’ It seemed to work, kept a strong business running (15 years at the time) purely on word of mouth because of the quality of their work and honesty in their approach. Different business, country and culture so not sure that works for you, but it also builds relationships sometimes to be blunt depending on who/what you’re dealing with.
That being said, I’d definitely hire an agency that puts ‘quality above all else’! Do advertise your mantra, whether you choose to use it or not, and even if you don’t always use it (like in such sticky situations).