BTW: in the EU there is movement towards mandating ISPs allow BYOD, including fibre ONTs.
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The benefit with an ONT (or even DOCSIS dumb modem) managed by the ISP is that they can do fleet upgrades much quicker as they don't have to keep all old protocols running. For instance the GPON -> XGSPON upgrade that some ISPs are running right now (or DOCSIS 3 upgrade) really only works well if you can turn off the old protocol which requires swapping out all ONTs/DOCSIS modems.
If customers bring their own stuff then you're stuck with these things for much longer.
But in cases where the ONT just looks like a media converter and you have a separate router I really can’t see any reason for the customer to provide their own ONT. Especially given PON is a shared medium so a misbehaving ONT can affect other customers.
That's how it works in New Zealand, but we take it a step further. The GPON/XGS-PON fibre network is run by a separate company[0] from the ISPs (and the company running the fibre network is prohibited from providing internet services[1]). So the ONT just functions as a media converter[2], and all our ISPs deliver internet over the same fibre network. This decoupling between the fibre network provider and ISP means you can change ISPs without any swapping of ONTs or repatching of fibre[3][4] (in fact, the process can be entirely automated, switching to some ISPs can take effect within an hour or two of placing the order). That and most ISPs allow bringing your own router (as there's no monopoly in the ISP space).
[0]: The NZ Government contracted four companies to build, own, and run fibre networks (three being new companies co-owned by local lines companies and the government to serving their local area, with the rest of the country being served by Chorus, the company that owns the country's copper network). These fibre companies are heavily regulated (including how much they can charge ISPs).
[1]: In fact, this requirement resulted in Telecom (the company that owned our copper network and who was one of the companies that provided phone and internet service to consumers) being split up, with Chorus being spun off, owning the copper network and owning the fibre network for the majority of the country.
[2]: Chorus did start deploying ONTs with a built-in router/AP a while back. They did offer this to ISPs to use, but uptake was very low, so it's since been discontinued.
[3]: I don't know how it works over in European countries where ISPs run their own fibre networks when switching ISPs, I assume they have to either install their own fibre line into the premises or the existing fibre is repatched to their network?
[4]: The fibre companies are required to offer use of their fibre network directly to ISPs, with the ISPs PON network running in parallel to the fibre company's, with the ISP providing their own fibre splitters and ONTs (which would be run on a second fibre line that each premises already has) and running their own OLTs. I believe this requirement still exists, but no-one ever took them up on it.
But I have read that some other communities that have tried the same model have had trouble attracting ISPs.