Can one ever really achieve a truly thick head of hair even after multiple FUE procedures?

The majority of hair transplant procedures are performed by
transferring hair follicles from greater density areas to balding or thinning
areas. But the number of grafts that can be harvested from the scalp is
limited. This is why you are noticing very minimal improvements in coverage
within the images you are referring to.

However, with Advanced Follicular Unit Extraction (which
requires more specialized FUE punches), it is possible to extract follicles
from the body to greater much greater levels of coverage. Body hair grows at
sharper angles and therefore requires more advanced forms of FUE compared to
head hair.

Patients, of course would need to have enough hair on areas
like the beard zones, chest, back etc.

It
is possible to create donor pools as large as 8,000-25,000.

The art (and skill) of hair restoration is to make it look like there is more hair in an area than their really is. A well done hair transplant you can come very close to an appearance of " full" but it may take a few sessions to achieve this goal. This is only possible provided there is good donor hair density. a few things to note:1) The hair density at the back of the scalp is about 100 follicular units per square cm.2) Our eye detects thinning at around 50-60 follicular units per square cm. the "exact" number depends on the patient3) each transplant session adds or builds about 30-35 follicular units per square cm4) if you start with a bald scalp and add 30 follicular units per square cm, it can often look terrific- if done properly.  will it look as dense as original? No. But if care is taken with the angles and selection of the hairs it can look great. That patient would go from bald to looking like they are "thinning" as you describe. Another session can be done to bring the density from 30 follicar units per square cm up to 45-50. At that point, the patient starts to really develop some thickness. But the entire art of hair restoration lies in making the density look more than it really is. 20 follicular units per square cm in a coarse haired salt and pepper colored Norwood VI can look amazing and cover alot of area. Your question is a great one. 

Restoration density varies from person to person and depends on graft size and donor density.   You can get close to natural density but full natural density is very hard to achieve in most people.  If any one promises you the full look, be careful. 

The answer depends on the extent of your hair loss. The FUE procedure does provide a natural but thin look in many patients with more extensive loss. The Fleming/Mayer Flap will provide uniform thickness much closer to the donor area in properly selected patients.