It's not common, but it's not completely unprecedented. I'm sceptical, and so are any amount of authors that you can find by searching for articles about BYOD.
I think your concerns could include any of the following, although no doubt many of them will be non-issues to you:
Have you understood the policy correctly? Do they definitely require you to supply the device, or do they just require you to purchase the device, but they'll reimburse your expenses provided you agree that the laptop belongs to them? Do they make exceptions for people who don't already own a suitable device, or who just aren't excited by BYOD and would prefer not to participate?
This is potentially quite a lot of money that they expect you to drop merely on equipping yourself to start work. But the same can be said of someone who has to buy suits when they start in a job that requires it, or has to buy a car for a particular job. Perhaps they're used to working with contractors (who far more commonly provide their own equipment)? If it's that they'd rather spend your money than their own then I would be extremely concerned: you don't want to work for an employer whose focus is not on enabling you to do good work, but rather is on finding ways to get you to pay for business-critical pieces of kit.
If you already have a laptop you potentially would use for this, then is it really suitable to work on? Does it meet the specifications you think you need for the job, or that they say you need for the job? If it's a high gaming spec then it might be irritatingly large/heavy/hot for work with too low a battery life, but if it's a lightweight home machine then "not enough RAM" or "not enough cores" are common problems when trying to use cheap consumer machines for development. Is your home machine even running the OS you need for work? Will you need to upgrade to Windows 10, or hold off upgrading when you'd prefer to do so? Will you need to virtualize Windows in order start using your device for work? Can you accurately assess how much of the spec that layer will eat up, or will it be a trial and error kind of thing, where you end up buying a new device for work after a week or a month? These thing all become your concern, because it's your money you'll have to throw at any problems that arise.
What rights do they expect to have to "your" device? Will they be happy for you to let your friends and family use a device that has their confidential data on it? Do they have compliance obligations, or will they gain them in future, that mean actually it's not possible for you to freely use "your" device any more? Will they require domain control or other access, and if so does that make using your laptop a non-starter? Supposing you quit or they fire you without notice, it seems unlikely they'll let you walk out of the door with it on the day. Remember Cary in "The Good Wife" with his personal laptop locked in his suddenly-former-office? That could be you.
Whose time is going to be spent maintaining it? What IT support do they provide? Does the idea of their people fixing your personal machine make you feel happy ("I don't have to do this") or anxious ("what if they don't do it the way I like?")? Who will be responsible for time that you cannot work because it's broken down? That might seem like petty clock-watching, but if it's going to take you an hour a week extra to maintain it, then that time has to either come out of your evenings or else the exciting project you want to work on, and either way this job is 2.5% less good than you thought it was yesterday. Take this into account when comparing this job to any other interviews that you might be attending.
Worst-case scenario, if you're careful, is that this is just a cost of doing business with them. Buy a laptop (or desktop, even, if you want not to be able to work from home). Mentally write off the cost, it's just an upfront fee to start this job, like a relocation cost they aren't covering. Use it exactly like you'd use one they supplied. Check if you can recover any of the cost as a business expense. If the fact you technically "own" it is ever any benefit to you then fine, otherwise it's just money.
Best-case scenario it'll all go fine. I used a personal machine for work when I was a contractor some years ago, I didn't buy a special one or anything, and it was no problem. But you can't assume it'll be fine until you check with them any issues that might be problematic. As a contractor I wasn't expected to give my clients any access to my machine of any kind, but many BYOD policies are more intrusive.
Btw, my views are probably influenced by being in the UK. The sales tax situation here means it's 20% more expensive for the employee to buy the same piece of kit, than it is for the employer, and that's before you even consider that the employee is almost certainly going to have to buy it out of taxed income whereas for the business it's definitely an expense. Our tax people are pretty strict about allowable expenses for full-time employees and if the employee owns the device it's really hard to justify it. So "employee buys a device they wouldn't otherwise have to" really makes no sense at all here financially: the employer potentially is making you pay £2 to save themselves £1, which is no kind of employer-employee relationship. It's pretty common with tablets and especially with mobile devices which the employee owns already and doesn't want to carry two phones. It's not common at all with machines for software development.