I cannot hope to approach
Alf's level of dexterity with the written word here, so I must tread carefully.
For the 'old' cockpit, I think that
Alf has 'nailed it' (as usual) in his statement that the solution to your dilemma lies in filtering out extraneous information. As an example, I have no interest in the Mach Number as we pass 20000 feet, even though it is on display, although it has my complete attention later in cruise at 37000 feet. The ability to filter appropriate and inappropriate information largely comes with experience. If I review my flying career, I believe that in my early days, I sought the minimum information required for safe operation. Now, 40 years later, I find that I'm constantly seeking more information, to enable more complete situational awareness.
A significant advantage of the 'old' cockpit, is that although, as you suggest, there may be an excess of information, information is predictable in it's location, that is, it cannot be moved electronically to another location as can happen in the glass cockpit. If the DME is in one location, and the Distance to Run to the next waypoint is in another, then that's where they'll stay, there's little room for confusion.
Alf's last paragraph was a chilling reminder to me of a fatal CFIT in our company -
e.g. EFIS might show the label ‘DME’ next to a DME beacon range and ‘DIST’ for LNAV range to a waypoint; given appropriate circumstances enabling human error, then these could be interchanged resulting in a loss of situation awareness.
In the case in point, DME
OR Distance to Waypoint was pilot selectable in the same display location in a 'glass' cockpit. Descent was carried out believing that DME was on display, whereas in fact, Distance to Waypoint was on display, resulting in CFIT 28 miles before the airport (No GPWS).
One of the modern 'glass' cockpit advantages is that much of the filtering is done for you, e.g. Localiser / Glideslope information will only display for the FMC destination airport. A further advantage, is that there's an OFF switch for most information, right down to raw data.
Once you've been married for long enough, you will become very skilled at filtering useful from totally useless extraneous information.
Regards (and apologies to Alf and my wife),
Old Smokey