That admixture is overstated; the vast majority of the Maghreb is still genetically indistinguishable from classical times. The Arabs successfully Arabized the Maghreb and Egypt, but the population remains unchanged in genetic terms.
There was a higher Arabian (identity-based) gene flow into North Africa than some populations like Lebanese, for example. We also have to consider that small infrequent of the DNA footprint can be Punic, and the Arabian peoples were not pristine but admixed with Levantines as well. So overall, I don't think it is correct to say that Arabization did not come with Arabian-identifying, genetically Southwest Asian, with possibly Levantine secondary structure (or vice versa). There was a mixing of people to a certain extent. And then you have actually highly Arabian higher frequency in some tribes in North Africa, of course.
What is Arab is a philosophical issue. Many Arabs that came with Arabian culture probably had Bedouin A (Levantine-like) profile with high Bedouin B (Peninsular-like) as well.
North Africa is a very structured place from a genetic standpoint with that structure having a diverse set of roots. It is true that there is a strong continuity over time, with some signatures tracing back to the Late Paleolithic, but we would be denying reality to say that things are monolith or that changes haven't happened. Internal regionalization alone over time with the genetic structure diversity will have them show differentiation not to mention processes of urbanization.
You have Libyans on the other hand who at some variation is of highly Arab ancestry. Those people will have amounts that top the other countries, and generally, the population will have a Northwest African to Egyptian gradient.
It all comes down to the region and other demographic/group localities and geographic parameters, natural topography that define group interactive behavior. An overwhelming amount of their DNA stems from pre-Islamic periods, that still stand.