Back Row and Sadness in particular slow the game down immensely; the mod doesn't require these unless the following are in play:
-) ATB Active/Full Speed is being used (this setting renders statuses like Barrier almost unusable and eliminates the benefit of high Dex)
-) The 7H Catalog version is being used with Menu Overhaul which can enable some unintended effects such as long-range enemy physical attacks, heavier Materia penalties, weak Limits, etc.
Physical damage has a lower output hit-per-hit but it's faster vs. Magic animations and the damage itself is propped up by both Critical Hits and Limit Breaks; but if Sadness is on, then Limit output gets throttled and you lose a big chunk of that damage. The idea is that physicals are fast but not versatile; you can only lock one (or two) elements onto a weapon using slots and most Limits are pure damage-dealers. Magic on the other hand can bring different elements to different enemy groups, but is slower to use and whittles HP when equipped (particularly Summons). Equipment drops/purchases play a part as well; if you get a Gold Armlet instead of a Silver Armlet or a Power Wrist instead of an Earring then that can lean things for a small chunk of the game.
To get physicals working, you need Elemental, front row (if they're not ranged), and to avoid Sadness for Limits. Even Aeris, who was being specced on her 'default' magic build for my test run, can hit high physical numbers with the right set-up:
For a more proper demonstration, I ran some tests in that area with Tifa vs. Aeris using the equipment I had available. It was fairly even in stat gains; Gold Armlet vs. Silver Armlet, Tier 2 spell vs. Cosmo Weapon, both having elemental 2x bonus, standard def vs. mdef balance (leans to higher Mdef for early game, slowly see-saws toward Phys defence by the end). For tilts, If Aeris had an extra +15 Mag from an Earring instead of a Star Pendant then she would have likely made an extra 100-150 per cast. Tifa, on the other hand, would have lost something like 50-100 damage if her Power Wrist was instead a Headband; like I mentioned, drops can create a tilt in certain places until it evens out again.
Fight starts at 0:43, rest is showing set-up:
In the vid clip, I show the damage output of both characters; Tifa is dealing comparable damage to a caster with tier 2 spells, is faster, and has Limits/Crits that can augment her damage. As a trade-off, she's on the Front Row which means she's more at risk from a KO; to avoid that, mitigation from Defend, Barrier, etc. can make this less dangerous. I kept the fight going into the 'powersoul' phase of the boss, which is very physical-damage heavy to show that frontline fighters can survive there (it's an extreme example though, PKeeper hits much harder physically than a conventional boss during this phase). So my advice would be to place more trust in front row fighters and let them do their thing without Sadness; if you have trouble with incoming damage, then make sure ATB is on Wait, maybe adjust the speed, and keep Barrier+All handy if you need that extra mitigation to make it safer. I try to make randoms not need Barrier, but there's a lot of unknown factors like RNG, party set-up, enemy formations, etc.
On the subject of Summons, magic-built characters tend to lose out on their Limits which mostly require Strength. I think of Summons as a versatile 'Limit' for casters that are elemental and can be used at any time, keeping up the versatility theme; at the cost of high MP consumption and being one-use per battle (also the HP reduction is a lot heavier at -10%). While MP can be recovered using Osmose/items, it consumes a turn that could have otherwise been used for offence/defence. A turn that a mage is using to replenish MP is a turn a physical hitter is using to deal damage.
I ran a similar test a while ago (should be an older post on this thread) where I tallied Tifa and Aeris' damage for a Jenova Birth/Vector fight and was quite surprised that they both turned out almost the same amount of damage despite the use of Summons, limited physical options, etc. So I don't agree that there's a heavy magical bias in the game, I think that it can appear that way, which is worrying, but on the whole both types are equally as viable as the other and I'd encourage a balanced approach so that fights feel more dynamic and faster.