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Apple’s replacement program is $99 for out of warranty battery replacement

Not really. The "estimated cost" on Apple.com is 139€ to 199€ depending on which company I take it.

You mean, other than Apple, where it is 99€.

If you want cheaper, iFixit is usually less.

Even if I sent it to Apple, which would mean 1–2 weeks without my phone, it would be 109€ ("estimated costs" per Apple.com).