Why do "Author's Rights" in "Consent to Publish" agreements allow pre-print publications? I have published in journal X and given them the rights to my work. In the &quot;Author's Rights&quot; clause, it says that I am allowed to post my work to pre-print servers (in the form immediately prior to publishing and sticking the copyright on) such as arXiv.
I am also allowed to distribute the copyrighted version for teaching and technical purposes, conference presentations, or other scholarly activities, and also allowed to post the copyrighted version to a personal website.
Here are my questions:

I can't understand the logic behind why I am given so many rights. Where does the journal make money? In what scenario does someone want to read my work and not very easily find a free way to do so?

I realize that if someone wants to cite my work, they have to cite the official version, which boosts the reputation of the journal. Is the main point that journal subscriptions negotiated with research universities have more bargaining power, based on impact factor?

I am planning on posting my work to a pre-print server while referencing the official DOI of the copyrighted version. It simply feels odd to me, even though I know it's perfectly legal.

What am I missing? I realize all journals are different, but I want to better understand why author's are given these rights. I feel like a copyright transfer is a big deal.

From my perspective, I want eyes on my paper. From the journal's perspective, they want money from my work. How are there so many subscriptions to journal X if it's so easy to get ahold of the papers for free?
Short answer: Pre-prints are not a big threat to the business models of journals and there are scientific norms that mean that journals are expected to permit pre-prints.
Longer Answer:
Why do universities and others pay for journals when some of the articles in these journal subscriptions are available via pre-print servers and other means?

Readers want access to the copy of record supplied by the journal.
Readers want access to every single article, not just the subset that are available as pre-prints.
Readers want efficient and consistent access.
Readers want an attractively formatted PDF or HTML copy.
Although not a pre-print server, it's also worth noting that universities respect copyright and therefore do not see services like scihub that provide more comprehensive free access as legitimate.

Why do many journals allow authors to share pre-prints?

They don't see it as a big impost on their business model given the points above.
Many journals have an embargo period on post-prints (i.e., pre-prints that have been updated based on the feedback provided by journal peer-review). These are presumably designed to encourage purchase of journal subscriptions.
Some journals may appreciate the importance of academic dissemination even where the potential readers do not have a subscription.
In some fields, pre-prints are very entrenched to the point that if a journal did not allow pre-prints, they might be seen poorly by that field and receive fewer high quality submissions.
More generally, there is competition amongst journals, and allowing pre-prints is one small way that journals can compete for submissions.
There has also been an ongoing debate about the business models of journals. Journals are receiving pressure from various parties to permit these forms of distribution.
Also, pre-print servers are generally non-commercial. I have seen some publishers ban positing on ResearchGate because they are for-profit and serve Ads alongside pre-prints.