I can give an honest practical answer I believe. I'll briefly give my background with Blizzard so you can weigh what I say and judge my level of bias for or against. The first Blizzard game I ever played was Warcraft 2 which was fantastic, along with the expansion loved it. Diablo and Starcraft came next with expansions, then Diablo II and its expansion, and eventually Warcraft III although I never did play its expansion. At that point in time I would say I was a reasonably big fan of Blizzard and came to trust that when Blizzard put out a game it would be very good, high quality and stable, and a fun multiplayer experience. We usually played the games with LAN play only, but did do a little bit of play through Battle.NET as well, although that was all before World of Warcraft came to exist and the various changes that have happened that bring us to current day Battle.NET. I have fond memories of those games and that timeframe and I still think that Blizzard makes quality games overall however...

World of Warcraft as good or bad as it may be - I have no idea because the subscription business model just didn't work for me personally with my way of gaming and my lifestyle so I opted out of playing or being interested in that game although several friends did dedicate their lives to it more or less. I have no regrets, it just wasn't my cup of tea. I did anticipate Starcraft II and later Diablo III from their trailers and past experiences with Blizzard's games but I wondered where they sat on the DRM front so I remained cautious. When it became clear that they would be using cloud storage and requiring Battle.NET for more than is actually necessary for a single player game experience I decided that I did not want to support that kind of single-player DRM experience and that I would no longer be giving Blizzard my patronage as a result.

I have no problems with gaming clients and even like the features they provide, but only the things that improve my gaming experience. I do not like some of the backend services that companies use that are either DRM outright or act as a way of controlling what the customer can or can not do, especially when it comes to a single-player experience. So I am not a fan of Blizzard's current practices which I consider to have anti-consumer elements, and as such I will not spend money on their platform personally as I do not wish to reward their anti-consumerism with my patronage. I'm a fan of their old games, fond of what some of the newer games look like, but that's more or less where I draw the line. I do not consider myself a Blizzard fan-boy.

I own Starcraft II only because friends desperately wanted me to play it and I stubbornly will not give Blizzard my money even though I did actually want to play this game. A friend bought it for me and so I do actually play it and enjoy it, and think it is a pretty great game. Still, I would not spend money to buy the addons or any other Blizzard games on principle, so basically if a friend wants me to play those, they're going to be the ones forking out the cash as I'm not a fan of Blizzard's anti-consumer DRM and other practices, but at the same time I'm not opposed to using the software if I haven't paid a cent for it, and it doesn't interfere with anything or cause problems.

So I do have Battle.NET installed and use it a few times a month on occasion to play Starcraft II. The software itself is on par with Steam, Origin, Uplay, Galaxy in terms of "weight" as most if not all of these programs are just Google Chromium web browser engine with a gaming frontend painted around it so they all use about the same resources and have about the same impact on one's system. The software is easy to install/uninstall, fairly easy to use and I'm not aware of it causing any problems or interfering with the operation of the computer or other software. I don't leave it running 24/7, just when I'm playing Starcraft II from time to time. I would not be opposed to installing and trying other Blizzard games if the opportunity arose (free promo, gift from one of my buddies desperate for me to play, etc.) but as I mentioned above - Blizzard wont ever see any of my money unless their games show up on GOG.com.

So I don't think you have anything to worry about as far as the Battle.NET software is concerned, it's more or less just Blizzard's own version of Steam client albeit much more simplified with less features. If you've got the opportunity to play one of their games for free and it seems interesting to try, I'd say go for it but I wouldn't recommend spending money there unless you're comfortable with the DRM and anti-consumer features like that. Some people are just opposed to software like that whether it is free or not, whereas I'm opposed to spending money on it but don't mind using it for free as long as there are no hooks and tendrils digging into my operating system (like SecuROM) for example and I don't believe they do anything harmful like that, at least not that I've determined.

So it really comes down to your ideology over such platforms and how bad you want to play the game(s) or get coerced into doing so, but I wouldn't worry much about the software causing harm or being hard to get rid of, I've not had any problems with it and I've removed it and reinstalled it a few times juggling disk space around etc.

That's about as objective as I think I can be. :) Hope that helps.