I'd argue one major reason you might choose to take this on a martial character early is because your accuracy/average weapon damage is already good enough for the challenges you're facing, and you want to mitigate the impact of bad damage rolls, especially with high variance weapons. This is especially the case with Gish builds that don't exclusively rely on weapon attacks: they can cast spells or cantrips vs high AC enemies, so they're unlikely to attack enemies that are hard to hit in the first place. They just want to make sure when they do hit something it actually hurts.
If you use it intelligently, Savage Attacker does scale (somewhat) with extra attacks. The following chart was made using the following strategy: If the first attack's damage roll <= the expected damage for the attack, use the reroll immediately. Otherwise, use the reroll on the second attack.
This can be especially relevant for Bladesinging wizards, who are likely to get high level spells before they're thinking about using an ASI for anything except INT. They're probably using shadow, and who use Shadow Blade for very high base weapon damage.
Cleric subclasses with Divine Strike (War Domain, Forge Domain, etc.)
(Any) Rogue
Wizards under the influence of: Shadow Blade (big weapon damage + advantage), Tenser's Transformation (gives advantage), Shapechange (big weapon damage), etc.
- Cleric subclasses with Divine Strike (War Domain, Forge Domain, etc.)
- (Any) Rogue, but especially Assassins (auto criticals on surprised enemies makes the reroll much bigger) and Arcane Tricksters (Shadow Blade)
- Wizards under the influence of: Shadow Blade (big weapon damage + advantage), Tenser's Transformation (gives advantage), Shapechange (big weapon damage), etc.
Flametongue
Dragon's Wrath Weapons
Frost Brand
Gauntlet of Ogre Power
- Flametongue
- Dragon's Wrath Weapons
- Frost Brand
- Gauntlet of Ogre Power
- Belt of Giant Strength (any)
Gishes
Characters who have good combat options outside of attacking don't mind that Savage Attacker is primarily good against low ACs. Against high AC targets, they are going to be targeting saving throws anyways. Since they will only attack when the enemy has low AC or they have advantage anyways, Savage Attacker becomes much better relative to an ASI.
In addition to Blessed Warrior Paladin builds fall into this category despite having Extra Attack. With cantrips as a reliable attack option, such Paladins can attack only when they have a very good chance of hitting and may take Savage Attacker over a STR increase after maxing CHA.
I've mostly tried to stick to single class builds here, as the possibilities when multiclassing can become ridiculous, but many multiclass builds could also fall into this category.
If you have a sizeable accuracy boost, advantage, no extra attack, and bigger than usual weapon dice, or alternative combat options for enemies with high AC, Savage Attacker will outperform an ASI for maximizing melee weapon damage. Actually doing the math for a specific character is the only way to know for certain which is better for them, but the more of these boxes you tick the more likely it is Savage Attacker wins out. The default assumption should always be "ASI is better" however.