No, weewx supports all kinds of interfaces including network depending on which gear you have.
Tom was likely suggesting the hardware datalogger because it 'is' pretty nice if you have the old console and can direct connect to the weewx system because of the logging and backfill functionality, but there are a lot of ways of connecting stuff up end to end.
There are a bunch of old WLL drivers if you google search for "weewx WLL" and poke around a bit. (wow - I wrote one too ages ago according to
https://www.wxforum.net/index.php?topic=41328.0 that I again forgot. Back then in 2020 a bunch of folks did initial versions.)
https://github.com/michael-slx/weewx-weatherlink-live seems most current and maintained. A quick search of the weewx map shows over 35 registered WLL systems so there have to be a lot more actual users. A quick look at the driver's installation web page seems to say you need to configure the ip address of the WLL device so weewx can talk to it over the network, so you probably are looking pretty good for a Vue plus WLL unless I'm reading it wrong.
I can't speak to whether there are lower cost options, but if it was 'me' considering I have the gear, I'd just do a Vue sensor suite and rtldavis using a rtl-sdr dongle and antenna (which I already have) so that gets it into the $100 plus Vue sensor suite kind of price range. WLL adds more stuff of course and is more turnkey at some large additional price. Really comes down to the time-value of your labor and blood pressure to integrate and support it all.