Let me start out by saying to me, riding the buses is fine, and I can't see myself using minivans under any pricing structure unless there is no alternative free transportation.
That being said, these kinds of comparisons are not exactly legitimate for two reasons.
1. If you have little kids, getting a Lyft or Uber with car seats that can fit your whole family is nearly impossible. So, if you need room for 4 or 5 people and need car seats, minivans are a great alternative.
2. Both Lyft and Uber use demand-based pricing. There are numerous times Lyft and Uber are extremely cheap alternatives. However, if you use them at high-demand times, the cost is much higher. So, just saying I once got an Uber for $13 is only half the story. Going from Magic Kingdom to AKL/All Stars/Coronado at park close is going to be much closer in price due to the demand.
For a single, a couple or even three people with a kid over the age of 8, minivans are not a good deal and do not make sense. For a family of 5 with kids ages 3, 5 and 10 who want a quick ride home at busy park close times, they are going to be a very attractive alternative at this price. And frankly, that's the target market because Uber and Lyft are not realistic alternatives due to the car seat issue.