Yes, and no.

One of those "Getting old is no fun" things is that your eyes ability to open up to an exit pupil of 7mm tends to go away

If YOUR eye will only open to say 5mm or 6mm (not uncommon in middle age btw), a 7mm pupil won't help with brightness - on a CENTERED eyepiece - where it does give you an advantage, of course, is that IF you are NOT looking through the center of the eyepiece, the larger exit pupil does help.

BTW, this all assumes that all lenses/prisms/baffles etc in the optical system are sized to fit the larger objective size. There have been more than a few pairs of "less expensive" optics made over the years where the limiting factor was not the objective size, but some other part of the optical train, but the objectives were made large as a selling point

Remember that is the maximum possible exit pupil, it's likely the optical design restricts the exit pupil to less than this - to reduce aberation. Although on good quality optics it will be as close as possible.

It also depends on the user. A pupil of 7mm is really about the maximum for a child's perfect and dark adapted eye. By middle age it is closer to 6.0mm even in the best conditions.
An exit pupil larger than this just wastes light.

A good estimate is pupil = 7.0mm * e(0.5 * (100/age)^2 ) for the geeks among us!

+1 There seem to be a good many different factors at play, some are easily quantifiable and some not. Larger lenses and better coatings help in theory but in practice you generally get what you pay for.

I've owned or at least played with a number of inexpensive binoculars over the years. Some were bad, some seemed great at first but with extended use I always found some major design flaw that detracted from the overall functionality. For example, some glasses offer good color rendition for the price but have problems with stray light or glare. Image sharpness and depth are for the most part subjective but extremely important when it comes to serious use. If the optics is just slightly out of adjustment you might not even notice it at first but prolonged viewing is going to be very uncomfortable.

I bought a 7x42 Zeiss B/GA Dialyt (later called the "Classic") for my wife on our first anniversary. She liked it better than a diamond. I think it was like $900, in 1994. Still our #1 birding binoculars.

7x42 or 10x50 porro-prism (the classic dog-leg shaped model in the picture) can't really be beaten for value for money.
You can make them with all spherical easy to manufacture elements and the prisms are relatively insensitive to errors.
They are a lot simpler to make than more modern compact designs so for the same money you (should) get better units.

After that it's all down to manufacturer's quality.
The main thing to look for when testing them is chromatic aberration - especially lateral color. Look for rainbows around the edges of high contrast edges especially near the edges - geometric distortion isn't usually important with visual use.

Remember that a German sounding name doesn't mean they are made in Germany (or Austria) and any extra 'features' like colored lens filters or built-in compasses usually mean poor quality.