No sweat. In fact, materia actually hampers your progress when you use it. The Two-Edged Sword sort of thing.
I saw a lovely graphic of the Nail Bat on the Internet captioned "Materia Slots are for Wusses!" This was a revelation, and an inspiration. I began the experiment forthwith.
Actually, it is so easy to play without materia, that I finished the game in record time (for me) while still enjoying all the side quests that did not involve materia. And there were a few surprises, too. It is not all straight forward.
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Cloud starts with materia. There is no remedy for this. But back at Tifa's 7th Heaven in the Sector 7 Slums, Barrett asks for help with the materia. After this, you can remove them at will. Watch the stats as you do this, and you will understand why materia is not always a good thing. Then they can be sold (usually for 1GP) or deleted.
You will need items to make up for the lack of magic. Some battles rely on magic. But plenty of items are merely magic in item form. Dazers, for example, are a wonderful thing.
Points to consider:
1--With no materia, there is no need to waste time stealing, mugging or morphing. You don't need all that stuff. There's more time to enjoy watching the fights themselves. I never paid much attention to how the various weapons looked, even though I knew they were all different, and that some even deviated from the norm for the character: Barrett especially has some very esoteric devices, and the corresponding moves!
2--With no materia to buy, you will have tons of money for weapons, items, or even that stupid little chalet on Gold Coast. Actually I found that I didn't need the chalet, after all. I just built up plenty of items from level-up battles.
Don't go crazy with the armor, either. With no magic, your limit breaks are all important in the boss battles. Just keep plenty of restorative items and be a little patient in battles. Some battles become routine, while others become rather scary. Especially where an enemy has an instant kill skill.3--Since materia affects all your characters' stats, you will immediately notice that your characters are much stronger than they would be with materia.
4--Unfortunately, if you love your little chocobos, you will miss them greatly. No materia, no chocobo. For you chocobo fans, it may be necessary to make an exception with Chocobo Lure. I made no exception.
If you simply cannot part with your chocobos, maybe you would be interested in the Chocobo Manifesto. Of course a real "chocobo-head" already know this one!
And no chocobo means the Ancient Forest will have to wait until the death of Ultima Weapon. Since Cloud's Ultima Weapon is dropped during that battle, the Apocalypse will already be superceded. However, the Minerva is a nice piece of armor and well worth the trip.
One special note regarding those Rilfsacs that are nearly impossible to hit: Bring lots of magic items, or better yet, equip your characters with weapons whose attack is 255 (Tifa's God's Hand and Vincent's Sniper or Long Barrel) and have at them. The rest of the enemies are wusses by the time you reach the Forest. This is an excellent place to level up, if you need it, or to achieve the higher limit levels before the North Crater.5--No materia means no summoning. Most battles move faster this way. Since some side quests involve summons materia, this may eliminate them. Condor fort's ultimate prize is materia, but other prizes are awarded from battle to battle. Seems rather random, but you can count on two decent weapons and a high level item or two.
6--Almost anything that "requires" materia to move ahead in the game can be replaced by leveling up, or learning the trick built in by SquareSoft. The first example I found was crossing the swamp to the Mithril Mine. You don't need a chocobo. The Zolom will knock out a character during battle. After it wipes out the remainder with Beta magic, one character keeps the group going, giving you a chance to run to the mine side of the swamp, usually unchallenged.
Some enemies have a magic side and a power side. Go after the power side first. For instance, Ying-Yang in the Shinra mansion seems nearly impossible to kill unless you go after Yang with your weapons. The default will usually be Ying, and Ying takes very little damage from most hits. Keep selecting until you are sure to hit Yang. Lost Number is the hidden boss behind the safe door in the Shinra mansion, and it also has a magic-sensitive side. Ignore it and fight exclusively with hits. Keep at least one person for healing and reviving. Set all limit breaks to the first level and the fight is a snap. Don't be afraid to use higher level items in any boss fight, as there will be plenty of opportunity to restock before the next boss.
And don't get stuck just on higher limit breaks, either. They may be less helpful than a lesser break, especially when magic is really the ticket. Diamond Weapon is another boss requiring magic. Items are perfect, right? No, because even high level items won't take many hit points. And many limit breaks are totally wasted. One notable exception would be Vincent's Death Gigas. The LiveWire attack works like Super-Bolt. And it's being used continuously, without waiting to fill the limit meter again.
7--Some parts were a surprise, as I said above. The arena battles seemed impossible before leveling up to over 70. After that, they went so fast, it was a disappointment. It was actually no fun, it was so easy. I went back and tried again at lower levels, say about 38 to 45, and they are much more exciting. With Xpotions from Wutai, and an emphasis on items and limit breaks, they are doable, indeed.
When Cloud is invited to fight in the arena in exchange for the Keystone, winning or losing doesn't affect the outcome of the game. In fact, Dio will award two accessories for success, but the ones I got I already had.
8--Because the stats rise with the Ultimate Weapons, don't be in a hurry to get them. I did hurry, and found that the challenges of the North Crater were greatly reduced. At that point, leveling up was unnecessary.
9--The final battle is easy with no materia, although it may take longer. I once accidentally went into the end battle with no magic, and wound up throwing money to win the battle. Even money is unnecessary with no materia. Once again, there is more leisure to enjoy the ongoing show of the final battle.
10--Occasionally this no-materia thing backfires. Barrett's Missing Score dropped his attack down to next to nothing, his stats changed to favor magic and killed several points off his strength. Unacceptable, and with no materia, even leveling up wasn't much help. Vincent lost some power, also. I am still experimenting with his. On the upside, Yuffie's attack took 9999 points each time, as did Cloud's. Watch all your stats carefully.
And last, I have not yet fought the American Weapons without materia. The Emerald weapon without the Underwater Materia.... Seems impossible. And I am used to Final Attack for the fight with Ruby weapon.
I'll be adding to this site again, filling in the details as I replay over the next few weeks in the North Crater.