To be fair nothing says an altered one can be used either. It seems to me it would be up in the air as a GM call.
I agree with this, but only to a limited extent. While the spell does not state whether a preserved piece of tentacle can be used, it does not say it must be fresh either. Do other spells specify either that a component can be preserved, or that it must be fresh? Many spells have components (fireflies, bat guano) which seem like they would need to be preserved, or would need to be gathered on a fairly regular basis.
As well, the rules must be read as a whole. The spell component pouch, by RAW, is assumed to have any material component except for those with a specified cost (this component has no cost specified), divine focuses and focuses which would not fit in a pouch. That includes the component for Black Tentacles. As a GM, carefully reviewing the rules to make my ruling, this tells me that, by RAW, the component for black tentacles is automatically in the component pouch, in adequate supply, easily restocked.
That doesn't mean I have to abide by that rule as written. However, it does mean that making the component difficult to access, expensive and/or requiring the players to seek it out is a change from the rules as written. In other words, it is just as much a house rule as modifying or banning the spell. I would also note that this should be communicated to the players in advance. The wizard would, in researching and learning the spell, discover that the material component is difficult to obtain. To me, if he cannot obtain a ready supply of the component, he can't practically learn to cast the spell reliably, so he would need to decide whether to seek out a supply to practice and master the spell (delaying its addition to his repertoire) or select a different spell and wait until he levels up again to consider that one.
Also, how rare are octopi in the game? I'd wager it is pretty rare unless you have some sort of under the sea campaign going on... AND let's say that people do catch octopi on a regular occasion. I'm pretty damn sure people willing to sell their tentacles are going to ask for a hell of a lot of money for it, which -again- you the GM get to decide. AND even if the wizard could buy the tentacle many times, what is the party supposed to do when the wizard runs out? Go back to the sea faring town to get one? Yeah, that is gonna make the other PCs happy, completely disrupting the quest.
Based on the rules as written,
giant octopi and squids are sufficiently common in the game that their tentacles, in a form suitable for use as a component of Black Tentacles, have a negligible cost, and are routinely found in adequate quantity in spell component pouches. Each of your comments above is a perfectly legitimate concern, the implementation of which departs from the rules as written, and is therefore a house rule. It is as legitimate as any other house rule, including one which says "material components are not assumed; no spell component pouch", or "Black Tentacles is too powerful to be readily available - you must quest to obtain the components and they are perishable" or "Black Tentacles is OP and is therefore banned from the game". None of those choices are inherently superior, and all three depart from the rules as written.
Also though, the GM can and SHOULD ban certain spells, or at least make them extremely hard to come by, perhaps even going on a quest to learn the spell. I still don't understand the reason everyone seems to think it's okay to ban races, classes, restrict items, but no one seems to ban anything that actually makes the game broken. Of course you can cherry pick spells to ban, but as for the materials, simply do not allow that feat to be taken (essentially banning a feat) instead of banning many spells. It always seems to me that people talk about optimization and all of that because they allow every damn rulebook under the sun. No gamemaster in his right mind should allow every single thing printed in the rule books. D&D gives you the ability to shape and construct your world, in other words the GM gets to make choices that reflect his world and how it works.
All of these are choices for the individual table. I find "Whatever ruling we decide applies to PC and NPC alike" tends to stimulate a very reasoned discussion as to whether a specific ability or combination should, or should not, be allowed, and how it should be interpreted.