In my field (tech) it's common for laptops to go home, in fact my company issued me a laptop backpack specifically so I could take it home. But the putative purpose is to work from home. So obviously this only applies to jobs where working from home is a reasonable thing to do. And indeed in my company, most people do WFH one day or another.
In fact, IT/InfoSec prefer that when you work remotely, you use company-issued hardware with company-controlled updates, antivirus and the like.
From an IT perspective, laptops cost twice as much as desktops, and last half as long, and are a far, far greater theft risk for a tailgater following an employee through a door and then wandering the cubicles stealing laptops. Such tailgaters are often hackers targeting company assets. As such, some companies only issue laptops to people they expect to WFH, and they actually want you to take it home (and really, everywhere with you), because if you leave it at your cubicle, it is vulnerable to tailgaters. Bizarrely, your house is much safer than the office, which puts an interesting spin on the "take it home" discussion.
Needless to say, when the laptop is at home, it does get used for personal stuff during non-business hours. And in tech, this is generally understood and tolerated. Not least because it's typically a salaried postition putatively 40 hours/week, but actually 45-70 hours/week with some of that happening at home. It might be 6:30 and you're embroiled in company emails and messaging, while also in a window Netflix is streaming some low-attention-required TV like Full House or Buffy's you've already seen. That's normal in my industry.
And IT is not going to care if you are playing some World of Warcraft on a Saturday at home on company iron, unless they have some InfoSec issue with you installing non-approved software.
But all this is done with a nudge and a wink. If an employee, by nature of their job, could only work in the office, and wanted a laptop only to do personal things at home, that is an inherently unreasonable request. If the company allowed it, they would choose to do it as an employment perk, and that itself might be a bit nudge-wink and not to be spoken of openly.
I pretty much assume that if they issue you a laptop, they want you to work from home and off hours. I'm guessing it's a salaried position.
Of course, I'm talking about the norm in my office. What matters is the norm in your office. And most especially what matters is that this applies to people who normally take their laptops home. Who, notably, isn't you.
Suddenly wanting to take the laptop home now, after never doing it before, will look like exactly what it says on the tin: aiming to take it on vacay for personal use at significant risk to employer.
So expect your employer to take careful note of whether you actually dialed into the VPN several times a day, and were reasonably responsive to important emails, messaging and other things you're expected to keep an eye on. They wouldn't expect a full workday on an approved vacation day, but they will expect you to keep your finger on the pulse. If you're not willing to convincingly do that, then don't take their laptop.