Reason #1: because it's cliché. If for no other reason than that, choose verbiage that your subscriber hasn't already seen from a huge number of other brands. Be different – use your brand's voice to speak to your subscribers in a way they deserve, and don't just fall back to the obvious and expected.
Reason #2: because it doesn’t make sense. You’re not actually welcoming them anywhere. The subscriber was just on your website a moment ago and is still on some kind of computer, using their inbox. They haven't physically entered into your email or your storefront, so you're not actually welcoming them to anything real. Say something more meaningful, like "Pleased to meet you" or "We're so happy you subscribed" (in whatever phrasing best suits your brand).
Reason #3: because it’s not worth the real estate. It’s fluff. Your home page doesn't say "welcome" when someone lands on it because everyone understands that website real estate is far too important for that. Email is a very profitable marketing medium, so don’t treat your welcome campaign’s prime real estate any differently than your website’s. The subject line, preheader, and hero area are the 1st content areas a new subscriber is going to see when they open your email, so use this space to say something valuable, interesting, different, and compelling.
Whatever you end up choosing, I recommend keeping it short and sweet to bait the user into opening and clicking-through to your site. With your subject line, you only have about 40 characters to work with, so make them count. Advertise the incentive they signed up for or include catchier copy to make sure you get the open. And remember to use carefully crafted preheader text to supplement the subject line in inboxes and capture the user’s interest.
*I do have one caveat. If your welcome series is greeting users who signed up to use your service – like an app or something else truly interactive – then saying “welcome” makes more sense. It’s still not the most creative phrasing – and it definitely still is cliché – but you’re speaking to a user who will interact with your brand in a more tangible way, so you can more easily make it work.