It's mainly about using the camera as a tool in extreme situations where user experience and preference and circumstance mean that very fine differences in operation may make all the difference to achieving the desired shot. Use or non-use of AE lock may be appropriate for different users and differing situations.
The effect on exposure and focusing is identical as long as the camera is set to lock both of these on half pressure. With many DSLRs, having either or both or neither lock on shutter half press is an option. Similarly, the AE button can usually be set to affect focus and/or exposure and to lock or to toggle.
AE can usually be set to lock only on pressure or to toggle the controlled parameter(s) on/off alternately and focus and or exposure may be able to be controlled. This adds to theaspects needing to be considered.
I'll use "shutter operated" for actual operation of the shutter mechanism below to avoid confusion of the term shutter-released and button-released.
The differences are minor but significant. To some extent it is a matter of preference and personal experience and both have their place. The differences probably only matter at all under extreme pressure at the outside edge of user and camera shooting ability.
The following modes are "denied to you" by using the AE lock feature:
With respect to multiple shots with the settings locked, this is also generally possible using shutter half-pressure but can take some getting used to. To do this the shutter is operated by full shutter button pressure, but the shutter-button pressure is then returned to half pressure rather than being released fully. This holds the locked settings and allows the next photo to be taken with the same focus and exposure settings. I find this immensely useful when you want a variable multi shot mode but slower than the auto repeat rate or at variable timing. This is to some extent an alternative to using tracking focus with the exposure locked and which is better is a matter of preference and circumstance.
If you like to work in "one armed wallpaper hanger mode" you may wish to set the shutter button to lock only one of the two functions, allowing the other to release after the shot when the shutter button is held and then using AE or some other option to reset and relock the second function. For example you could lock and hold focus with the shutter button but not exposure, allowing the latter to be altered and then locked with AE button or some other button. This requires the brain to coordinate several fingers with he shutter finger needing to be partial-travel controlled and would not be usual (but, you did ask :-) ).
Why would you want to do that? One reason MAY be to allow tracking something that held focus position but was moving through a zone of variable lighting. This would be a rather extreme case and not usually preferred.
If you use AE lock it takes an extra finger operation to release it, which is one more factor (amongst many) setting the outside edge of what you can achieve in a given time in utterly extreme shooting situations.
Camera stability and ability to hold user-attention on the job at hand and to track a "target" (especially a fast moving one such as an animal or surfer or gymnast) is affected by using either AE lock or half pressure. Which way it is affected is again a matter of preference. I much prefer using shutter half pressure as it allows all control in the index finger without extra time or thought to access the AE button, to the extent that I never use AE lock, whereas others may value the lack of need to hold button tension in absolute extreme situations. (Time i a vanishingly small consideration once the preferred functionality becomes burned into the brain).
In a tripod situation of a fixed scene, or where a scene is not going to change for some seconds until a critical moment arrives (head turns, bird flaps, diver dives, ...) and a shot will be taken, perhaps with a "cable release", use of AE lock may be preferred to maintaining half pressure for an extend period. An alternative is to swap focus to manual mode and to accept the minimal penalty of exposure 'calculation' at exposure time, ot to use AE toggle, but this too is a preference.
Other similar and subtle considerations could be thought of.