The same is true for power lines. They're mostly privately owned. The power utilities are subject to various regulations (rate regulation, etc.) but the wires were built with private money and are private property. In contrast, most water/sewer lines are owned by the municipality, and paid for by the public through taxes and hook-up fees for new construction.
This is not and has not ever been true.
Here  is an open auction with ~$2 billion in federal aid attached - "a total of $1.98 billion for 10 years." This was last updated just over a week ago. I would dig further back for other subsidies, but it is not necessary. Through tax breaks and subsidies we (the government, tax payers, etc) have certainly aided infrastructure build out for telecom cos.
There was some tax dollar funded subsidies in the ARRA, but it's a vanishingly small fraction of the trillion+ dollars invested in telecom infrastructure in the last few decades.
Is this one of the taxes that they just throw straight onto my monthly bill?
Two, AT&T is paying the tax, but the government is mostly kicking the subsidies back to small rural telcos and coops. Telcos with more urban footprints, like AT&T, subsidize telcos in high cost rural areas.
So calling CAF a subsidy to AT&T really makes no sense. It’s like saying Apple would love the government to slap a 5% tax on iPhones and kick the money to providers of low cost phones. Even if Apple could increase prices to compensate, and get some of those subsidies for the iPhone SE, it’d still be worse off than without the “subsidy.”
The FCC doesn’t disclose USF contributions by company, but you can guess: https://apps.fcc.gov/edocs_public/attachmatch/DOC-303886A3.p.... Total reported telecom revenue is about $300 billion per year during that period. AT&T averaged $120 billion per year in revenue during that period (about 40% of the industry). (This is probably an overestimate because AT&T’s revenue includes non-telecom revenue.)
During that period, USF revenues were $7-8 billion per year. 40% of that is like $3 billion. Even if I’m wrong about AT&T’s revenue share by a factor of 4 AT&T still pays in much more than it gets out.
Also, it's likely eminent domain attempts for Google's benefit would run afoul of the law. I don't think the government can eminent domain something for the benefit of another corporation.