Like I said before (and made a little post about it), the balance of the 5e has shifted. Today I’ll analyze the possibility of dumping your primary ability score and which class fare how well with that.
Weapon-Focused Builds: These are the classes and builds, which shines by using their weapons, especially in combat. These would be the barbarian, the valor bard, some cleric builds, fighter, paladin, ranger and rogue. I’ll just count the monk in those, too, since his whole body is a weapon.
The math is simple, since you only have either STR or DEX as abilities and we’re mainly talking about attack and damage rolls. I searched throw my materials (DM-Base Rules, Hoard of the Dragon Queen + Supplement) and the highest AC I got were 20 (Helmed Horror (Challenge 4) and Roper (Challenge 5)). Even the Adult Dragons made it only to 19 and even though 19 is there several times, it’s still the minority.
As long as your character have proficiency, he has a 10% chance of hitting the highest AC for monsters for now. And even without any ability modifier, you can hit a lot of common monsters, which aren’t suppose to be heavily armored. In fact, humanoids are more of a problem here.
In the end you should have some ability modifier, but I personally think, that it won’t hurt as much as some might think, to actually use only 16 or 18 as a target stat. Even though DEX-Builds are far better off with 20, since a high DEX has several benefits, like AC in light armor, initiative, more skills and checks and a common saving throw. Here it just sums up to multiple areas, where DEX is benefiting you. At least until you get a -5 attack and +10 damage feat, because then you’d better have the best accuracy you can effort. 😉
The higher the level gets, the more you’ll feel the difference in damage, but since it mostly takes just 1-3 more hits to kill, you might consider it to be doable.
Skill-Focused Builds: I’m not only talking about some class, but the true wish to be a skill monkey. If you want to be up on your skills, be a jack-of-all trades, it’s just better to stick with your primary ability at a decent level (14 or 16 depending on other factors) and spreading the rest out. You’ll be good enough in what you do, to don’t be a burden in combat, but are better prepared than most when facing unknown challenges.
Control-Depending Builds: Not only spellcasters falls into these, but every build which have features depending on DC. Every point helps, sure. As long the features might trigger lesser effects when saved you might consider to stop at 18, but if you mainly use those, who have no effect on save, do yourself a favor and push the DC by aiming for max. The highest monster saving throw (for now) is +13 by the way. So even maxing out makes it only a bit harder.
Damage Casters: Those who uses spells to make the most damage, its a mix of the logic of Control-Depending and Weapon-Focused builds. But spells with attack rolls of 1st level and higher are more valuable than a weapon attack, while most damage spells which demands an saving throw deal at least half damage in case of a successful one. So aim for the higher if attack rolls are made often, while you might consider to stop at a at least +3 bonus when you have the option of relying for saves (since they are much less reliable without proficiency).
Support Casters: You can mainly dump your primary ability score, as long as your class don’t use features which relies on that. Playing a Wis 10 druid might be strange, but if you go for Moon Circle and only wants all those buff spells and out of combat magic and a little bit of healing (even though having a modifier would make a small difference here and a big one at the amateur and beginner tier), you might think it’ll be worthwhile to have decent DEX and CON for cases, you don’t have Wild Shape anymore or are beaten out of it.
My conclusion is, that having a high stat is a boon, but most can actually aim for 16 and never really needs to raise it further to be effective. Of course it makes them more effective, but in the end you might consider to rather raise another score or use feats instead of pumping your ability score to the max without thinking. Some benefits aren’t as easily calculated as an attack roll or save DC and the probability to hit or save.
Keep your eyes open for new possibilities and try something you want instead fear to need.