Yes indeed. They are always looking for command potential. I am not aware of anybody who recruits pilots where that is not a consideration. It doesn't always result in that potential being realised, but it is a selection criteria.
Recruitment has traditionally come from three sources. These come under two broad umbrellas of "Experienced pilots" and "inexperienced pilots." In the case the former, two of the three sources are civilian pilots and ex- military pilots. Both of these groups will have significant experience relevant to their backgrounds.The civilian pilots will be from an established background and the main training commitment is likely (where relevant) to involve conversion type rating training. Cost savings are to be found in those pilots already type rated. Unfortunately this is sometimes interpreted (particularly on these forums) as desirable without relevant experience. That simply isn't true!
Military pilots also come from an "experienced" background. Usually type conversion training is involved and although rarely a problem, there is also the transition from a military culture to a civilian one.
The third source, and relevant to these forums is the inexperienced recruitment. Over the last Twenty years that source has grown in importance and to some extent has displaced some of the experienced resource groups. This "cadet" recruitment can be expensive and extremely demanding of available training track resources. For that reason alone (and there are many more) it is important to ensure the Calbre of background training of the candidates is fully understood, verifiable and something (in many cases) the airline is directly involved with. It is also likely the customer airline will minimise their financial risk exposure by utilising training schools that consistently present the right product.
The wings alliance website claims a statistic that older and mature FOs stay with their first airline for longer compared to younger pilots. This makes sense as we are generally more settled with a family to consider and so stability is more of a priority when it comes to job satisfaction.
I am not sure who they are, but it is not at all unusual for an airline to want you to be based temporarily or permanently hundreds of miles from your home. Even then, further base changes may be a requirement of being promoted or maintaining employment. As you know military life often results in unaccompanied detachments and it is not at all unusual for ex-military experienced pilots to want a stability that often just doesn't exist in reality. For an inexperienced recruit "cadet" it is simply par for the course. You recruit them where you want them, and move them as you need to. It is further up the seniority lists that the problems arise because naturally people expect more stability commensurate with their seniority. Stability for new recruits is often a bit of a pipe dream. That is just one example, never mind the realities of "roster stability" and job insecurity etc.