I argue that, although it is less true in 5e, it is still the case. Especially because casters have the tremendous upside of versatility. And in my opinion, it will always be the case because of the fantasy of swords and magic that we have in our heads.
If by 'we' we mean 'people who have played D&D for a long time,' sure, I suppose so.
Dreams&Pixies said:
As long as d&d has such high-fantasy magic, the gap between fighters and wizards is unlikely to ever be bridged.
You say 'as long as,' but the gap's already been bridged. In 4e the Fighter & Wizard were reasonably balanced.
5e did not restore LFQW entirely. It restored part of the lavish spell progression to wizards while taking away virtually all limited-resource abilities from the Fighter, but it also scaled spells with slots rather than caster level. And, it also restored the 1e fighter's multiple attacks, problematic in their own way.
OTOH, 5e scales save DCs with character levels when 3.x scaled saves with slot level, and TSR era D&D didn't scale save DCs, at all.
The 5e fighter improves with level, basically, about every 5th level he gets an extra attack, that's the main thing. It's nothing to sneeze at, it's 'linear,' though any damage bonus he gets is essentially multiplied by the number of attacks. The wizard also scales his cantrips every 5 levels, and they start out, and stay, weaker in terms of DPR than extra attacks, and there's not a lot of bonuses available to add to them. There's more of a range of what cantrips can do than what weapons can do, but it's not huge, so on the at-will side there's this gap between the two. Spells fill in that gap.
At first, two 1st level spell slots do so, and it goes up from there. It takes the wizard's higher level slots to really step up and deliver excess damage to make up for the difference between cantrips & extra attack over a full 6-8 encounter day, so if the wizard only ever got 2 or 3 of his top slots, it'd probably just end there. But, of course, he keeps his lower level slots, which stop mattering so much for DPR purposes but still give him ever-growing added versatility. Then there's rituals.
Thus, the wizard stays Tier 1 as it was in 3.5, while the fighter, as a competent DPR specialist rises to Tier 4 - or even with judicious use of backgrounds & feats to expand out-of-combat competence, arguably Tier 3 (purists might point out that 'builds' aren't supposed to factor into Tier).