I don't mean this to sound like an attack, but you're conflating two separate issues.
EA is a business that has revenue projections and a stock price driven by meeting those projections. So yes, they have an incentive to create enough tension in-game to encourage you to spend money on something you enjoy playing.
I have a lot of respect for F2P individuals as I've never been able to resist the competitive itch to send a little coin EA's way in order to accelerate my progression. There is nothing preventing you from being a contributor to your guild. The challenge is the focus. F2P is simply going to take longer to be a strong contributor, but in my (125mm GP guild) we don't ask F2P to work on toons for every phase of HSTR. We ask them to focus on a very specific phase with a very specific group of toons that we expect them to spend all resources on. Phase 1 is a perfect opportunity for F2P guild mates to excel. Save gear, ability mats, zetas, and currency. Grind out First Order and the Vets. Get JTR in the next release and voila, you have a phase 1 and arena viable team. Both of which will advance your gear and crystal accumulation so that you can advance even faster.
The issue you're encountering, and one I run into often, is the anxiety of the grind between point A and Z. Focus narrowly. Hoard relentlessly. Ignore the woman in the red dress. You're always going to be behind the P2P, but the P2P finance your ability to be F2P. Can't have it both ways.