That's what I disagree with.
You need a good roll in your prime score to meet basic competency and need to continually boost your primary scores to maintain it.
No you don't, at least not if the DM follows the guidelines for difficulty.
5E is extremely forgiving and because of that a comparitavely low roll character is mathematically still competent.
In 2014, they leaned too hard on simplicity of mechanic on many classes. This put too much pressure on primary score, feats, and fighting styles to maintain basic competency at anything but a defender.
Not true and I routinely play martials at high level that never get beyond a 16 in their attack stat, including several 20th level games. As a matter of fact I personally usually do not making my attack stat higher than a 16 at all on a martial, I am usually boosting a spell casting stat first, or taking feats that give me spells.
The designers created a system where your either need good rolls or higher level dominance to fill any role other than body blocker, defender, healer.
This is completely false in 5E. It may have been true in other versions, but it is no longer the case.
Your STR14/DEX14 fighter/barb/pally doesn't have a supporting fighting style for both their attack options and if they attempt to level both STR and Dex equally, they will fall behind the curve.
"Behind the curve" is not the same as "incompetent" and if that Paladin really wants "power" she should put all her ASIs into Charisma, because spells and abilities beat weapons in 5E all day long in combat and spell casting stats beat Strength and generally beat dexterity out of combat.
There is a mathmatical standard out there about the "baseline" damage being a Warlock who starts with a 16 Charisma and Hex and takes ASIs at 4th and 8th level. That is considered the "normal" or average damage for a damage dealer. The 14 fighter you mention can easily do half of that baseline all day long and that is without even trying to optimize. If you optimize that fighter who starts with a 14 strength and dexterity will equal or beat that baseline.
And in this discussion let's remember we are talking about damage which is an easy metric to compare characters but a poor one to measure power as doing damage is generally weak in combat compared to effects or control and is useless out of combat.