> if it's so easy and cheap to host a relay

That wasn't asserted anywhere. Quite the opposite: as I explained above, the expense is why few people have done it (and even fewer have done it in production). It's the PDSes which are (relatively) cheap and easy to self-host.

> why then "Free Our Feeds" initiative [0] looking to raise $4,000,000 [1] to establish a second relay [2]?

Per the section you cite, they're doing a lot more with that money than running a second relay: they're spinning up an entirely separate organization independent of Bluesky to develop ATproto and applications using it. That includes, but is nowhere implied or explied to be limited to, the "second relay" they mention.

In any case, even the self-hosted relay described in that above-linked blog post (let alone some RPi under someone's bed) is in all likelihood a long ways off from one that's even remotely production-ready. There's no mention of redundancy, no mention of future-proofing, etc. It's reasonable to assume that the "second relay" would be multiple such relays, likely on machines with even beefier specs - in other words, at least as capable as the existing Bluesky-managed relay. I'd also be unsurprised if it expanded to a "third relay" and "fourth relay" and so on.

Further, there's more to running a relay than just the hardware; you need someone to maintain it. $4 million pays for 40 employee-years (assuming every employee is full-time with an annual salary of $100k). That could be one sysadmin for 40 years, or an 8 person team for 5 years, or a 40 person team for 1 year, or what have you. Free our feeds claims they'll need $30 million over 3 years, i.e. $10 million per year; if half that goes to salaries, we end up with a napkin-math-guesstimated team size of 50 - which is about the size I'd expect for an organization that wants to independently maintain a bunch of technical infrastructure, develop applications, prod whomever needs prodded to get ATproto formally standardized, etc.