You need to have an Insight on only 6 characters for MOST days and 10 characters to cover ALL days of ABX and ABL.

There are a total of 14 rounds of ABX and 14 of ABL, Round 1 and Round 8 can be played twice a day as it falls on the weekly reset. So you can play Alliance Battle 32 times every two weeks, and you only need 10 insights to cover all of them. I will use the term 'usage' instead of day because you need 2 teams per day, one for ABX and one for ABL.

No Brainers

These are characters which are the only available supports for at least one usage in either ABX or ABL.

1. Cyclops: He can be used 5 times. He is the only available support 3 out of those 5 times.
2. Taskmaster: He can be used 4 times. Abomination also covers all those requirements but is a worse pick than taskmaster.
3. Proxima: She can be used 4 times. She is the only available support for Alien Villain ABL. Morgan is a decent alternative who is a better support than Proxima but covers only 3 usages. If you have a surplus of Insights, I'd suggest putting one on Morgan if you use Wanda instead of a PVE Jean in Universal Female ABL. Proxima does not support Wanda.
4. Ghost Panther: Must-have for Universal Male ABL and Universal Hero ABX. You can also use Phyla here but GP and Nova are the best supports here. Equipping the insight on Nova works too but he is clearly a worse support than GP.

You miss 1/32 runs if you don't have an insight on either of these two:

1. Phyla-Vell: Must-have for Universal Hero Female ABX.
2. Beta Ray Bill: Lead for Thor in Hero Alien Male ABL.

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These 6 characters cover 17 usages out of 32 in two weeks.

Optionals

If you use T4 widow for ABX/ABL:

• Shuri: She can be the insight provider in 11 usages.
• Dazzler / Polaris: I would suggest Polaris since she can be used in WBL and GBR as well.
• Sif / SheHulk / Valkyrie: 2 usages
• Mystique / Black Cat / Green Goblin: Speed Villain day (Can be a skip for you if you don't want to give an insight for 1/32 usage)

If you use Shuri/Kamala as a Dealer instead of T4 widow:

• Valkyrie: She can be the insight provider in 6 usages.
• White Fox: 7 times, all of them for Shuri or Kamala.
• Dazzler / Polaris: I would suggest Polaris since she can be used in WBL and GBR as well.
• Mystique / Black Cat / Green Goblin: Speed Villain day (Can be a skip for you if you don't want to give an insight for 1/32 usage)

Efficient utilization of Insights

If you use Black Widow as a dealer in ABX/ABL, the characters who deserve an Insight most are (in the order):

1. Shuri: 11
2. Cyclops: 5
3. Taskmaster: 4
4. Proxima: 4
5. Ghost Panther: 2
6. SheHulk / Sif /Valkyrie: 2

These guys cover 28 of the 32 usages ABX or ABL days. The other 4 characters are almost skippable if you do not wanna use an Insight for one usage in every 14 days.

If you use Shuri as a dealer instead of Black Widow, these are the characters:

1. White Fox: 7
2. Valkyrie: 6
3. Cyclops: 5
4. Taskmaster: 4
5. Proxima: 4
6. Ghost Panther: 2

Note: For No restriction, the only supports I have included are Shuri or Valkyrie since they give the maximum amount and using anyone else makes your score comparatively lesser.

This also means that as long as you have 6 insights equipped on these characters; all your other insights on characters like Wave/ Sif AND Valkyrie/ Mbaku are redundant if you have equipped them just for ABX and ABL.