I have played around with this, and I have had the same results.
In my opinion, the AI could use a little assistance---such as manipulation. When programming these attacks to happen, it is almost better to have multiple missions, each with just a few potential targets. You can order the attacks so that they go after the top target first. One trick that I learned is to put the lowest priority target at the end of multiple missions. In this case, one mission may never attack, but another might. That way they do eventually get to it.
The AI is NOT perfect. It can be persuaded/tricked/manipulated into doing what you want it to do in several different ways. Some are better methods than others, and it seems to depend on each scenario. So, you have to test and test again in order to make sure that it does what you want.
For example, I set up a SEAD Patrol mission. It worked fine in one scenario, but doing the same thing in another scenario didn't seem to work as well. In the scenario that it didn't work so well, I replaced the SEAD Patrol with a one-time Support Mission, using the same a/c and load out. This time, the Support a/c attacked the target the way that I thought that it should. So, my point is, the game is so complex that things don't always work the same because the circumstances are different each time. So, if one method doesn't work well, try another.
With regard to your question, I enjoy using multiple missions. I use small numbers of attackers and targets. I do believe that in real life, pilots are probably assigned to a specific target, while others are assigned to other targets. If that's the case, then multiple missions makes perfectly good sense, even though it is more time consuming to do so.