I'm a day late and like 10 pages behind, but I want to examine this. A Fighter who's high enough level to do a 3d10 Fire Bolt is high enough level to get three weapon attacks. So how does that compare? It really depends.
Let's consider one extreme. A sword and board Fighter who dumped Dex because they're in plate armor pulls out a non-magical longbow. They're making three attacks for 1d8 each with a terrible attack modifier. Compared to that, a Fire Bolt with even small Int bonus is superior. But would that ever happen?
Any Str focused Fighter wanting a ranged option is far more likely to pack a Thrown weapon than a longbow. Let's say darts, for minimal extra encumbrance. Now it's three attacks for 1d4+5 each, which is higher average damage than a Fire Bolt and with a better attack modifier to boot. The Fire Bolt would have a greater range, but that's a narrow niche case to spend a feat on. And any sort of magic weapon designed for throwing would tip the scales even further.
There are several issues with this analysis,
First, strict RAW an 11th level fighter can usually only make one attack with a dart because she can only draw one dart on a turn unless she has the Thrown Weapon fighting style (which a melee oriented fighter typically doesn't). To make 2 attacks with darts she would need to start her turn with one of them in her hand already. To make 3 attacks she would need to start the turn with 2 darts in her hands.
Second, the normal range on thrown weapons is very short. Most of the time you are throwing a weapon you are going be doing it with disadvantage due to range. Not all the time, but more than half of the time and there will be quite a few times the enemy is completely out of range. Most ranged attack cantrips on the other hand will go out to 120 feet without any disadvantage. The only time you would normally be throwing a dart without disadvantage is if the target is more than 10 feet away and less than 20 feet away. If he is closer than 10 feet but more than 5 feet you would be better off using a whip.
Getting Hex, Eldritch Blast and Toll The Dead through Magic Initiate is going to be a bigger buff for most strength-based fighters than extra attack will be for most full casters. Keep in mind, you get extra damage for an hour (or until you lose concentration) when you cast Hex and since you are primarily a melee build, that means if you don't use it in melee to boost damage, it will be available in those fights you need to go ranged.
Niether of these examples are particularly powerful combat feats. Extra attack will not generally be a very powerful buff to a full caster and magic initiate will not be a very powerful buff to a non-caster (although it will typically be more powerful than extra attack would for the caster). The main reason why is the action mechanics. Extra attack will generally be inferior to other things a caster will do with her action and using cantrips will generally be inferior to other things a non-caster can do with her action in combat.
On the whole, cantrips are not better than weapon attacks, and this is by design. I really ran into this when I was theorycrafting out an Eldritch Knight using the playtest rules. Swapping one weapon attack for a 2d10 cantrip is not much of a gain, because the weapon attack is adding an ability modifier and likely a magic item bonus. Swapping multiple weapon attack for a cantrip is a straight loss. Cantrips are weaker than a Fighter making their normal attacks because leveled spells are stronger.
With War Magic, an Eldritch Knight can do both a cantrip and an attack at every level where she would have extra attack except at level 5 and level 6. Because of this, using a blade cantrip for an EK is substantially more powerful at level 7-10 and generally still more powerful from level 11+
Given that this is a thought experiment though, I assume the alcohol I initially used to make it seem balanced would wear off before the next session and I could apologize to my players after coming to my senses 
