Some thoughts:

Developers that take longer to develop are less active but do not need less-frequent agitation. Just the opposite in many cases.

Initial agitation is to ensure even absorption of the developer by the negative and to get rid of the initially high amount of by-products. I agitate more at the beginning of development than after the halfway point.

The amount of agitation (if one can even quantify that...) plus the development time = the total amount of development for a given developer. Increasing agitation while leaving time the same is the same as increasing time but not changing the agitation: the overall contrast of the negative is increased. Most of us like to increase time for expansions since it is more controllable and repeatable.

After 50% of the development, most of the shadow areas and mid-tones are developed almost to where they will be at the end of the developing time. It's the highlights and more dense areas that continue to increase in density. The amount of increase with time is proportional to the amount of exposure with more exposure areas developing more than the lower. This means that agitation in the first part of development is what affects the lower-exposure areas more. If one wants evenness in the shadows and lower mid-tones, then a fairly regular agitation early on seems to be logical.

Agitation schemes that use reduced agitation do so for particular reasons. Compared to continuous agitation, reducing agitation to a certain point, say, every 15-30 seconds, has little more effect than extending the development time a bit since the developer is not exhausted in any of the negative areas and the by-product build up is not significant.

Extending the time further (and the exact point this happens is different for different developers, etc.) results in the developer running out of activity in the denser areas of the negative while remaining fully active in the less dense areas (BTW this would happen more quickly in weaker developers, i.e., developers that needed longer developing times...). This results in the compensating effect, which reduces the development of the highlights proportional to density and allows squeezing a bit more information onto the negative. This is the primary reason for most reduced agitation schemes. The more one reduces the frequency of agitation, the more pronounced the compensating effect. The risk is getting uneven development and mottling/streaking.

Another reason for reducing agitation frequency is to get edge effects. On a micro scale, the same mechanism that causes the compensation effect will cause developer in denser areas adjacent to less dense areas to exhaust. However, there is a bit of diffusion of developer across the border between the two areas of differing density. This results in the edge of the dense area being infused with a bit of more active developer, creating a thin line of greater density along its edge. The opposite happens to the edge of the lower-density area, it gets some of the less-active developer which results in a thin line of reduced density along its edge. These lines are adjacent to each other and lend the prints made from these negatives a more contrasty line of definition between areas of different densities creating the illusion of more sharpness or even outlining of forms. These are called Mackie lines and are clearly visible in my grain focuser (I use PMK with a reduced agitation scheme for the last half of developing just to get more of these edge effects. Reducing the agitation in the first half of developing results in uneven development).

So, I would think that an agitation scheme should be chosen on the basis of 1) getting even development, 2) getting the compensating effect one wants (or none at all), and 3) encouraging formation of or preventing edge effects.

If one wants no compensation and no edge effects, then continuous agitation will work just fine, just with a shorter development time than, say, agitation every 30 seconds.