Yesterday I for some reason got this extremely strong urge to replay Xenoblade Chronicles X, and while doing that I figured I might as well try to help the wiki out with by filling in missing mission information such as prerequisites, so I decided to do all missions as early as possible including basic missions.
So after Chapter 2 I started doing the missions (since that's when they start to become available obviously). The normal missions went by no problem since most of the information had already been added to the wiki (there was just a few small things I found) but then it came to the basic missions. I accepted all the available ones and even double checking multiple times to make sure I had them all.
After having done some of them I went back to mission control to double check once more and a whole bunch of more missions had been added (and no I'm not mixing up the cleared missions that gets re-added) so I accepted them and once again made sure I had them all and headed out to tackle some more and after a while I decided to double check on mission control again and guess what, even more new missions had been added (I was level 12 at the time and the prerequisites listed here on the wiki for the ones out of these missions that I did before realizing what was going on said that you needed to complete chapter 3 before they would become available which I hadn't done, so I decided to level up to level 13 and check if any more basic missions had become available and sure enough there were.
So long story short, basic missions becoming available arent affected by how many chapters you have completed, rather by your level. Of course there are some exceptions susch as the New Orders missions and the Off the Record ones as well as basic missions leading you to certain normal and affinity missions. Discovering a continent could also be a potential requirement for certain basic missions (I haven't left Primordia yet on this save file so I can't verify that just yet)
(Update): Turns out that after I completed chapter 3 a whole bunch of new missions had become available even though I hadn't leveled up, but one thing to note about them is that they were missions related to other continents (at the very least Noctilum and Oblivia (still haven't left Primordia on this save file b.t.w.)) so it could simply be that you need to complete chapter 3 to get access to missions that lead to other continents it's either that or basic missions outright has an extremely complicated system that just give you new missions whenever it feels like it. (Edit): There were Sylvalum and Cauldros missions there as well. And another thing I thought off was that all those basic missions could have to do with the party members joining aftef chapter 3, especially who is level 18 when he joins.