I've seen a number of Ts and currently work at the front desk of a counseling center. In my own experience, most of my Ts have had evening availability, which is when I go. The only exception was when I was in college and could easily see the a T on campus during the day. My current T says she likes working late, which works great for me.

Working with Ts professionally, it is really hard for them to be away from their kids and spouses. Some only work during the day and some work a lot of evenings or even weekends. The ones who are most flexible don't have kids and aren't married. The student Ts can only be there when other Ts are, so that impacts their availability. As for the ones with families, even two late nights a week really impacts their kids. One is a single parent, so she just can't do late appointments. Another one has very young kids and if she stays late, she doesn't even get to put them to bed, so she'd only would get to see them for maybe an hour max in the morning. It's just not fair for them to sacrifice their personal lives for others or they may start to resent the clients they stay late for.

With my job, it is really really hard to do an appointment that is not 6pm or later or on a weekend, but if that is all my T had I would just have to make it work. I've done it twice when I needed emergency sessions. It's worth it to me. I know some of our clients come in first thing in the morning and go to work after or others come over their lunch break. With kid clients, little ones will typically come over lunch and eat at the office or during gym/art/etc, while older kids have priority for after school times. You just do what you gotta do and/or find a T who has hours that work for your schedule.

[edit] also, I had a previous T I used to see around 5pm or so, but when she needed to move things because of stuff with her kids, I happily worked with her on that. I didn't want to be the reason she couldn't take her toddler trick-or-treating on Halloween.