Is attaining a house even possible in full servers?

[Kenky]

why was the plot system even made instead of having infinite housing areas?

because, back when FFXIV entered its 2.0 state (ARR with Yoshi-P), it was quite expensive to get even a small and it was a rather rare thing to obtain. There wasn't enough people earning millions of gil, or could save up that amount.

Jump forward a few years and the changes piled up. More wards, Personal Housing option, Cost reduction, The large player-boom when Stormblood launched. As a result of -all- of these, players began to be able to now only buy houses, but purchase multiple plots on one character. That quickly became a problem and as the last by-product, we got given the Placards Hidden Timer system. Something that I feel the entire playerbase hates with a passion.

We all currently have to deal / suffer with the actions players made in the past and our constant bickering and knife-wielding towards other players for having what we don't.. Isn't really winning SEs trust back.

But why the wards over infinite housing? Two main reasons. 1. Yoshi-P (and other developers at SE) want a Neighborhood-esque feeling for Housing. 2. Infinite housing (with the system the way it is) is near-impossible. It would need to be through the Apartment system, rather than the ward system. Actual physical land in a virtual world will add up if everyone has it.