When I was a kid I played a lot of games of empire with my dad, and both of us ended doing exactly this - there was almost no incentive to make anything other than infantry, transports, and planes. We played on huge maps almost exclusively, so anything that took longer to get to the front probably wouldn't get there in time for it to matter. Now I usually use wide and short maps with a horizontal wrap so that the fighting is more linear.
I think EDCE helps fix this with the addition of antiaircraft guns, but they can still be overwhelmed by a larger group of planes - which are cheaper and more mobile than the antiaircraft guns. An antiair costs 1.5x a plane, and the plane has added value due to its speed.
This brings us back to the original problem - it's often easier and more effective to just throw more of the same units at things they're bad at fighting, rather than bring in or produce units that counter them.
Another 'problem' is that empire focuses a lot on expansion. Infantry, transports, and planes are the best at expanding because they're the cheapest and fastest units. Expansion is the obvious priority early game, but the shift from expanding your domain to protecting it from threats when they appear doesn't involve much change in behavior. Mostly, the player just directs more units to wherever the threat is.
The AI isn't really good enough to pose a threat to a player because they don't direct their forces in a very focused and sustained manner like a player would. The only real incentive to use the specialized units to fortify an area comes when you are fighting an opponent that would direct sustained resources to you, such that you
1. expect to fight over the same area for a prolonged period of time and
2. have to care about the cost efficiency of each round of combat.
Even then, making something other than infantrytransportplanes is a hard choice because throwing more stuff at the enemy just works.
I don't like every situation in a game having the same answer, because the whole point of a strategy game in my mind is to adapt different solutions to whatever the situation is. I've just barely started tried to fix this, and what I came up with is to scale the counters way up. The effectiveness of a unit in its 'role' should be very high, but so should the costs of ignoring that role and throwing it at something it isn't supposed to fight.
Planes in my games are now very good at attacking, but bad at defending, especially against fighters.
Infantry are good at taking on structures like cities and airbases, as well as defending, but are bad at attacking armor.
Armor fight well against other ground units but are only mediocre at killing dug-in infantry and poor at taking cities.
Antiair and heavy artillery are now time-consuming structures built by engineers, so they don't take up a city's production line but still aren't practical to spam everywhere.
Ships are mostly the same but the small ships like transports or patrol boats do very poorly against larger boats - medium boats can fight larger boats at a slight disadvantage, but the disadvantage for planes and ground units is much sharper.
I then decreased the time for engineers to create infrastructure like roads, minefields, ports, etc. to encourage their use.
The hope is that all of this creates a gradient of undeveloped frontier areas where infantrytransportplanes rule the day to more developed and better defended interior regions where shore bombardment and missiles become more useful while infantrytransportplanes will get killed if they rush in without help.