You stated the reason why mid-facelifts and lower eyelid surgery are often performed together, because of the potential for the lower eyelid skin bunching and causing more wrinkles under the eyes than prior to the mid-facelift.
Just because they are often performed together for good reason, ultimately each person's face is different and their past surgical history is also different. If a surgeon follows a cookie cutter approach to all faces, then there is a risk of performing unnecessary surgery and with each additional surgery additional risks apply.
If you smile, it is similar to a mid-facelift. When people smile the cheek rises and the lower eyelid skin can bunch and wrinkle. Not all mid-facelifts performed by different surgeons are equivalent. You are not buying a shirt at one GAP store, which would be the same at another GAP store. Instead each plastic surgeon is like a contractor. Depending on which one you choose, you can get very different results.
Some patients who have had bad lower eyelid surgery with ectropion, or lower eyelid malposition already have had too much lower eyelid skin removed. Some reconstructive eyelid plastic surgeons will perform a mid-facelift alone to help push the lower eyelid upwards to improve the post lower eyelid complications. I have seen one patient who had a lower eyelid and mid-facelift combination have a problem when she opens her mouth, the lower eyelid pulls away from her eyeball. When she doesn't have any facial expression, it looks fine, but obviously this is not natural, and for this patient the cosmetic improvement was not worth this post-operative problem.
If the mid-facelift is performed conservatively, and taking into consideration the fact you already had a lower eyelid surgery in the past, I can see why one of the surgeons did not recommend it.
In general, I am not a big fan of the mid-facelift procedure and prefer volume restoration of the transition area of the lower eyelid and upper cheek using either fat grafting or fillers, depending on the patient's age and facial aging issues, and preference for surgical versus non-surgical improvement.
I am also not a fan of aggressive browlifts either. I wrote an online article titled, "To Browlift or Not to Browlift that is the Question" explaining my thought process.
Be careful, do your research, and good luck on your plastic surgery journey!