This could be a problem, but only if I had interviews or even just a phone call from a recruiter. But I'm not even getting to that stage. I just get rejection after rejection via email for every type of company and position I apply for.
Dozens of rejections, and you get to a point where it becomes a waste of time to even apply. Also, many of the job postings are clearly fake; companies like Capital One, JP Morgan, or NBC, just to name the first three companies that come to my mind, have been advertising the same positions for months, if not years.
What happens is that you fall out of the loop and become invisible, if not an outcast that no one wants to touch. You reach out to your network and you receive cold indifference; all the "friends" you thought you had are not interested in providing any factual support (e.g., strong referrals). Basically, it comes to a point where you are begging for attention and some support.
What's discouraging is that there are so many people in leadership positions who have terrible leadership skills or competence. Not that it's something others should think I possess, I'm clearly biased in this case, but they certainly don't have it.
The world is what it is, and plenty of people get laid off and are able to get interviews and find jobs. I am certainly in part responsible for the situation I am in (not in the sense that I did anything shameful or despicable, in the sense that maybe I should have spent time developing a network different from the one I have), but it is not a fun situation to be in.