Gevlon asked why he should invite other pilots to his corporation. I suspect there is also an element of asking why should he endorse others inviting pilots to other corporations.
In essence, there is a "large POS" fuel bill to be paid, of roughly 500m/month. This bill is the same whether covered by 1 pilot or 7. Why not allow others to pay your fuel bill for you?
Pilots will pay for division rental and POS research slots (especially ME and copy slots). Pilots that have a safe home will often take advantage of PI, and pay additional taxes. Depending on the month, this ranges between 400M and 600M for a Foo corporation.
I am sympathetic to Gevlon's question. Inviting a pilot to your corporation is to trust them to a degree. In Eve, trust is not a desirable attribute. At no times more undesirable than when you are under a wardec, and it is not merely (protective) paranoia making you think someone is out to get you.
No one needs to be in the same corp to run missions, mine, haul. These are all roles done very easily out of corporation. Today, I ran some wormhole anomalies, with 3 different corps involved. It made zero difference what corp we were in, especially with mobile depots to refit.
What a corp does give, is the ability to use facilities in a POS. These facilities are valuable to players, and those players are willing to spend ISK to use them. We charge per division (manually), for research slots (game mechanic), and for PI tax (mix of manual and game mechanic); with the goal of ending up in front of costs, with a small margin. We don't charge for simply being in corp and using bookmarks, SMA's to refit and PHA's; though these are also valuable services.
POS permissions are not easy to understand, but we have used them to good effect; and prevented a known theft/awox attempt from taking anything of value (and they ended up taking nothing because they didn't want a couple of industrial ships). Better POS permissions would allow me to grow the Foo corps size rather than the number of Foo corporations, but we take what we are given, and do the best we can with it.
In a 1 player corp, the player has to bear the entire cost of running the POS by themselves. For some that is trivial. For others it is a huge 'tax' on their activities. They might be trying to plex 1 or 2 accounts, and the cost of the fuel is 30% to 50% of their income.
There are other ways to subsidise this cost. I did try reactions using gas that other corp members farmed and I bought. I ended up shutting this down due to lack of profit. It however can go some way towards paying for some of your fuel bill.
Many corps use a wormhole buying program, so that those with 'moving things' skills can do that, while others who prefer other activities can do so. While this does not need to be done in a corp POS using divisions, it is more convenient and more secure to move large items directly into secure storage, especially as this can be done while one player is offline. Such services can be charged for, and the Foo corps charge a small margin on this.
Due to wardecs, the Foo corps are not currently recruiting. F2P is another industry minded alliance that I have relations with that are recruiting (in game channel F2P). However, if you are willing to set up your corp in a similar manner to ours (preferably without the wardec) and want some assistance or advice, please either evemail Dotoo Foo or drop into the "FooPub" channel.