Here are my 2¢.
In your particular case it seems that you regularly face situations like this one, since that's the case my first piece of advice is:
- From the first meeting, tell the client that the size of their logo will be considered in the overall design. If they want the logo bigger after seeing the design(s), you will take into consideration their feedback but you strongly suggest the size of the logo will be proportionate to the general design system.
One good thing about a problem like this, and this is VERY hard to understand for both junior and seasoned designers, is that this is an opportunity of charging more for your work. Since I usually charge by the hour, these kind of situations are actually situations I look forward to, because I can charge more.
The second piece of advice is made of two ideas:
- Tell this to the client: We can certainly increase the size of the logo, but in the big scheme of things is not about how large the logo is, is how often it appears throughout your website and your other branding materials.
- A powerful strategy to convey ideas is by using metaphors. In this case, tell the client the increasing the size of the logo is like going to be movies and sitting in the front row: you see everything but you miss everything, both at the same time.
Hope these tips help.