Get over it
When I had my first GUI based computer at home, I knew the Company green-screen system was doomed. It was more intuitive, I was more productive, I quickly started taking home work because I'd get it done in half the time. The core technical support teams complained about security, support & fitness-for-use. Didn't matter, people could see the most portent benefit - they got things done faster.
Fast-forward about 20 years. In that time I've done 1st/2nd/3rd Line, built Apps & Architected complete IT solutions. I think I'm aware of the so-called 'issues' from both sides. So, here's some thoughts:
Security (1) - stopping people taking work info? Are you nuts? I dare you to tell me that you cannot think of several ways to work around that issue with so-called locked-down kit, start with email & work your way through to Network Drives that happen to be on your home network - of course, if you work in Defence or someing it's different but, the ultra minority case does not prove the overwhelming majority fact: any member of staff who wants to get info out, will.
Security(2): - malware et-al. When was the last time you saw kit without modern AV/Firewall/anti-phishing software on it? More importantly, will you tell me you've never seen malware get through into a Corporate system? Really? Well I have (at 3 separate major global IT giants, to say nothing of their customer networks). Don't kid yourself that yur corporate security systems are anything better than the commercial equivalent - in fact they probably ARE the commercial equivalent. When my 70-odd year old Mum tells ME that she's just had the latest version of Norton installed, I know that security systems are in the public psyche!
Support: apart from the ease at which it's simply stated that anyone going BYOD must have some kind of support in place - or (even more likely) simply state that if they don't have the kit they can't do the job, ergo - why are they still working here? The support issue - what's its outcome? That workers can't work coz their kit is down? Have you seen how long it takes an internal support team to fix a broken laptop? The despair starts when the Automated email response tells your that your non-working kit comes under the "72-hour" fix policy (if yur lucky!!), then when you finally get to a room somewhere (never at your own office) they look at you as if you died in the night & say "oh, it will take a day or two to get to - we will ring you". Bah, I cannot believe that some IT folks have the nerve to state that technical support is an essential element.
Bottom line - BYOD immensely popular with the people who pay your (IT is a support function, remember?) wages.
The reasons generally cited for not going BYOD are specious at best.
It's happening. Get over it. Better still, find a way to support the folks going there - that way you may not be marginalised
<dons flame-retardant coat>