Mostly a non-problem.
Jet bridges are adjustable across a standard range of heights. The 707 & DC8 cabin door sills were within a couple inches of each other and that set the original standard in the early-mid '60s. The 727 was the same height as the 707. The 737 is a foot or so shorter, but even the latest ones being built today are the same height the original baby 737-100 was.
The DC-9 and subsequent derivitives MD-80, MD-90, MD-95, & Boeing 717 are all ~2 feet shorter than 707 standard. So just a bit shorter than the 737. Those were within the adjustment range of the early jet bridges
The 747 came next and set the height standard for wide bodies which was considerably taller than the 707/DC-8. That forced the replacement of a bunch of jet bridges, mostly at the major international gateways. The cabin doors were wider too, so bridges & cabs got wider also. But this stuff was all changed back in the 1970s. Almost all the new taller bridges that were installed in response to the 747 have themselves been replaced simply through old age and failure. Or have been updated / upgraded.
A couple years after the 747 the DC-10 and L-1011 joined the fleet. Taller than the 707/DC-8, but shorter than the 747. So within the adjustment range.
Next came the 767 & 757 which share the same sill height and sat slightly lower than the L-1011/DC-10. So again within the then-standard adjustment range. At about the same timeframe the Airbus A300, A310 and later A330 & A340 came on the scene. At roughly the same height as the DC-10/L-1011.
So overall, from the very late 60s until the mid 90s not much has changed on the high or low end. There have been two developments in the last 20 years that have been putting pressure on infrastructure. The A380 lower deck sits a little higher than the 747 does. So for the comparatively few gates world wide that see A380s, the jetbridges need to go farther upwards.
By far the bigger issue numerically is the advent of RJs that sit real low. At many airports those are still boarded by walking across the ramp. At other airports the ordinary narrowbody jetways are knelt down as far as they go and a steep half-assed ramp is attached to the end to descend the last 4 feet down to the RJ door sill.
Terminals designed for RJs are also being built differently, with the boarding lounges at ground level and mini jetways that slope up the 3 to 5 feet to the door sill height. Rather than the 707 standard which has the passenger lounge on a tall second floor 25ish feet above ground level and a jetbridge sloping down to the aircraft door at 8-10 feet above ground level.
The 787 series sits above the old 707 but below the 757/767. So it’s not an issue.
Airports that don’t see the real tall 747 & A380 won’t have jetbridges to accommodate. If it’s an airline-served airport at all it probably has one set of very tall stairs for just-in-case use.
We have a list of approved diversion stations for each aircraft type. Bringing a jet into an airport that’s not equipped for the type can be the start of a multi-hour or -day nightmare for all involved. Do they have appropriate stairs, cargo unloading equipment, tugs and towbars, etc., etc.
The bigger and more exotic the aircraft, the shorter the list of acceptable divert airports. As an example, my carrier’s list of acceptable divert stations for the 757 is about 100 airports in the US. The 767’s list is only about 40, despite them being sorta twin sons of different mothers and very common aircraft in the industry for 3 decades now. The 737’s list is over 200 but the 787’s is just a couple dozen so far, albeit more all the time.
Our approach to emergencies is not “find the nearest concrete”. It’s “find the nearest acceptable concrete & services”. It’s only the really Hollywood-implausible scenarios that would persuade us to land on the nearest concrete with no other considerations.