I personally wouldn’t because by burying the stem there’s a good chance rot could happen, those bits aren’t meant to be burried. Overtime once the Agaves get big you won’t even be able to see those parts that are bugging you.

The one in the first pic I would suggest a pot twice the size of the original pot it was just in. Heck maybe even bigger than that. Normally with succulents I like to suggest to take it slow when uping the pot size, but Agave and Aloes are different. They can get big and root bound in no time. The little Agaves still put in a small pot, their roots haven’t taken off yet.

So the beheading succulents doesn't apply to agave?

You can behead Agave. The big guy you can cut right around where the brown stem meets the oldest leaves. A good spot to cut on the middle Agave is right where you drew the line. The smallest Agave I wouldn’t cut yet, too small and you could run the risk of it just falling apart. There’s just not enough there.

GF - the leaves probably didn't dry up because of a lack of water, it's more likely it was the result of natural senescence (aging). As you have probably noticed, many succulents with scale-like leaves tend to keep extending, growing new leaves at the apex of the stem and losing the oldest leaves at the most proximal end of the foliage mass. IOW - it's normal.

There should be no problem chopping your plant back and planting it deeper, though I can think of one caveat. If you are using a grow medium that supports perched water (PW), it is highly advisable that you make sure the roots and particularly the lower stem, are not low enough in the pot the roots/stem are below the maximum ht of any perched water table (PWT) that exists after a thorough watering.

The pots above are filled to the top with grow medium. The shaded part in these images illustrates the presence of a PWT and how the depth of the pot, while having no effect on the max ht of the PWT, impacts the amount of remaining soil in the pot that can be considered "safe" for roots that have a tendency to react poorly to wet/soggy conditions. If a grow medium supports a PWT, the max ht of that PWT is a constant. IOW, no matter what the depth/ width/ shape of the pot, that grow medium will always support a PWT with a predictable max ht. Roots and stems of any succulents being treated as a cutting should be planted so roots and stems are above that maximum ht; better still, would be using a grow medium or utilizing a growing arrangement/ technique that eliminates PW altogether.

Most succulents readily form adventitious roots from nodes along the stem where leaves were formerly attached, so there is little chance of the stem rotting unless the propagule is of a species that rots easily unless cuts to roots/ stem are allowed to callus before the propagule is stuck, or, the propagule is planted so deep it's roots/stem are forced to deal with soggy soil and the absence of free oxygen which accompanies it, which sets the table for any of a number of fungi that prosper under the conditions described. These fungi are often gathered loosely under the umbrella of 'damping-off diseases'.

..... back to your cutting - it would be helpful to leave at least few roots attached to the bottom of the stem when you repot deeper, but it isn't necessary - just shortens the time it will take the plant to resume it's normal routine and rhythms.

Whenever I repot succulents with scale-like leaves, I use a scalpel to clean up all the old tag ends of dead tissue, and I pay particular attention to areas where the distal end is dry/dead but the proximal end where it attaches to the plant is still green. This is the most likely entry point for fungal infections, other than a severed stem or roots/stem in soggy soil.

Al