Gaming without battery on laptop?

Hi. 

I have an Alienware 17 laptop bought in late 2014. A few days ago, even when plugged in, the laptop wouldn't charge anymore. I Googled around a bit and found out that one way of figuring out whether the battery might be the culprit, is to remove it, and then plug the laptop in. If the laptop then works, then indeed the battery needs replacing. 

Now that's exactly what the issue seemed to be. Here's the thing though; I play World of Warcraft on my machine and I always have it plugged in (if I don't, the battery drains within 30 minutes, so there's really no use). My fps usually sits around 30-40 on a 5 out of 10 graphics setting. Which I always found highly disappointing, considering I bought this laptop so I could play the game EASILY at full settings. 

However, now, having taken the battery out of the laptop and just running it on the power cable, I seem to be able to play World of Warcraft at 50-70 fps at a 10 out of 10 setting!

My question is; considering I always play with the power cord plugged in anyway, is there any downside to just not bother buying a new battery (which seems to be going for around 140 Euros) and thus having no battery in the machine, playing it just on the power plug? And I mean as in, can it be in any way detrimental for the computer; I don't really care having to be plugged in in order to be able to use it. 

Thanks for your time!

Kris