Its not uncommon for people to go with your second pick and start two arts together, particularly if your dojo teaches two arts. My first martial arts school taught both Judo and Karate and there were people who signed up for both and started training in both arts at right away.
My school teaches both Taekwondo and Hapkido. Now, we have 24-25 Taekwondo classes every week and 1 Hapkido class, so I'll let you guess what the focus of the school is. I started Hapkido a few months after Taekwondo, and I didn't find it hard because it was 2 arts, but simply the amount of time. I got more invested in Taekwondo (up from 2-3 classes a week to 4 classes a week) and I wasn't conditioned enough to also do Hapkido, so it dropped by the wayside. When I was conditioned enough, I had started helping out, which meant I was doing 20+ classes a week, and the Hapkido class kind of went on hiatus due to lack of people.
Since Hapkido started back up, I've been going regularly. The only other regulars we have already have their black belt in Taekwondo. Those that tried to do both at the start burned themselves out on one or both.
We have a lot of other students who are mildly interested in Hapkido, especially women who go to our school to learn self defense. However, most people want to get their Black Belt first, so they only have to focus on one art a time.
I can see how starting two arts at the same time can slow learning if both arts are similar, for instance if you train in Karate and Tae Kwon Do simultaneously that might slow learning but not with arts that are radically different. Both Karate and Tae Kwon Do use hand strikes and both Karate and Tae Kwon Do use kicks and so the different way the hand strikes and kicks are done in both arts can cause confusion and slow learning, but Karate which is striking based and Judo which focuses on throws and grappling, since the arts are so different, I don't see how starting those two arts together would slow learning in any way, shape, or form.
There's also time and money invested. Let's say you take classes 2-3 times a week, and you practice at least 3 hours a week on your own. (Let's take Karate and Judo as the 2 arts here). If you're just doing one art, that's 5 hours a week devoted to Karate. If you take Karate and Judo, then you need to go up to 10 hours a week of practice to become just as competent in both of them. If there are any conflicts between the style (i.e. stances, footwork, how you hold your hands) it can take more to train yourself for each style.
Even within a style you can have differences. There's a HUGE difference in how we teach our demonstration team vs. our sparring club. For the demonstration we want deep stances, we want the techniques held long enough for the audience to see them, beautiful extension on the kicks, and pristine technique above everything else. For sparring we want shallower stances for more speed, closer kicks that focus more on speed and contact than on strength and beauty, and hands held up to protect the head instead of tight at our side for the best looking form. We had a girl in both classes and she was very good at both, but she did have to be reminded "your kicks don't need to be beautiful in sparring, they just have to hit" or the opposite in the other class.
Going back to the time investment, if you take 5 hours a week for karate, but you only have 8 hours total you could devote to martial arts, if you add in Judo you're either going to suffer at Judo because you only get 3 hours in it, or you're going to suffer in both if you cut down the time invested in both to 4 hours. This is an arbitrary number, but the point is that there is a finite amount of time per week, and people might not be able to train in two.
There's also the financial aspect of taking two arts, sometimes it's easier to add one activity at a time. There's also conditioning - can your body handle practicing that much each week?
Now, if you're in good shape and have tons of spare time, then sure. Take them both. But sometimes that's not an option off the bat.
