You're not likely to see any benefits, at least none that outweigh the problems involved.
A mundane problem, but a serious one. Humans already have notable difficulty giving birth, and large babies cause particular trouble; some mothers die in childbirth even with modern technology and medicine, and in pre-industrial times that rate was significant. An egg that must ultimately contain such a baby is guaranteed to be even larger (unless you want smaller and less-developed babies, thus effectively premature babies, which poses a host of issues like much higher rates of infant mortality and mental problems) due to the need for the enclosing eggshell if nothing else, never mind any nutrients or other materials that might be left over. That makes all those potential complications more likely and more severe.
I don't want to see the consequences of trying to give birth to a baby that is unable to fit through the birth canal; that would be a common cause of death for egg-laying humans without other drastic changes. Widening the birth canal may seem to be an obvious answer, but the design of human hips is a compromise between walking upright and giving birth; a wider birth canal, especially to the required degree (probably at least 50%, because the egg has to hold a human baby and have a shell thick enough to offer actual protection), could seriously impair a woman's ability to walk on two legs.
Animals that lay eggs and abandon them do get to scatter many potential offspring, but most of those eggs will be smashed. This is a viable strategy (see R-selection versus K-selection), but that is not conducive to anything resembling civilization. Animals that guard their eggs, on the other hand, have one parent basically glued to the nest from laying to hatching (which would be months for humans); the care this requires does reflect the possibility of intelligence and civilization as we recognize them, but that puts a heavy burden on whoever is not tending the nest.
Pregnancy and live birth, by contrast, make protection relatively trivial. It can be seen as carrying the egg or eggs within the mother's body instead of leaving them outside it, which reduces the problem of protecting the offspring into simply having the mother protect herself, something she would be doing anyways and thus is not an added cost. It also saves the expenditure in energy and materials of creating the eggshell, another point in its favor.
How, exactly, is a human baby going to crack open an eggshell from the inside? We are born rather weak and frail, without any convenient sharp claws or the like. Our skulls are still very fragile, so breaking out with any hypothetical added appendage to the head (a special tooth or horn that falls away after hatching, most likely, but I'm open to suggestions) is going to involve a lot of battering against the shell from the inside, likely causing permanent brain damage. Keep in mind that larger eggs are naturally going to be thicker (read: harder for the baby to break open), to offer more protection: too thin, and the weight inside would crack it just from falling the few inches between the mother's body and the ground.
Besides, on hatching, they're still going to be helpless for a very long time. Many egg-layers have offspring that is at least mobile within a few days; if you want your humans to match that, their offspring will have to undergo significantly more development before hatching than normal humans do before being born, which requires a larger egg to hold the larger baby, which in turn feeds right back into the size problem! Also, there are studies that suggest our level of intelligence requires a long period of effective helplessness while our brains develop and learn, whereas species that are born with more development are also more limited in learning capacity; I can't prove this point, and you could probably get away with ignoring it, but it's still something to consider.
Egg-laying works for some species, but bipedal intelligent humanoids would most certainly not be among them, at least not in anything nature might produce. You say that genetic engineering is involved here, removing the question of evolution, but you'd still need a reason why they would do such engineering to change humans to what (for humans) gives every sign of being an inferior mode of reproduction.