I can see a reason - but I don't know if it's the reason. Probably nothing to do with it. But I gotta tell a story to get to round my reason:
A couple of months ago I compared the tab bars in detail on the big five browsers to see how much space each one allocated to the text part of the tabs. I looked at the gaps between tabs, the gaps within tabs, the behaviour of the favicons, the use of ellipses ( or equivalent ) and the use of the close tab icons amongst other things.
What prompted me to do this? I was a Chrome user, I'd got into the habit of opening more and more new tabs. With every new tab, the amount of visible text on each tab reduces. But I wanted to see whether any of the browsers allocated more space to the tab text as you open more and more tabs.
Some of the big five have configuration options that improve their behaviour, but I was looking at out-of-the-box behaviour. And as it happened Chrome came out the worst - by far.
For example here's Chrome when things get real tight:
and here's Opera
Now ok, so I don't actually let my tabs get that small, but nevertheless Chrome does not prioritise text (or favicons) as much as the other browsers seem to.
So Chrome was starting to annoy me - to the point that I actually switched to using Opera, since it's behaviour with smaller tabs impressed me. [Yeah - easier to change browser than to change my own behaviour, right?]
But's let's take a step back - is it really Chrome's fault I got to be in this place. Well maybe a it, but really it's my own fault that I got into this habit of opening a new tab every time I wanted something new. It seemed easier to do this than examine the tabs I had and decide which one to reuse. [Every now and then I'd get exasperated and close the lot and start again.]
Instinctively I'd say I need a tab management system, but I'm unconvinced - I don't want the baggage of having to 'manage' my tabs, I just want to go to web pages. Tab management systems, in my mind, are like new fangled to-do apps where you spend more time using your to-do app than you do actually do-ing stuff. Result - it doesn't get used.
So coming back to the New Tab button. My theory is that there's something about Chrome that makes it oh-so-easy to open more and more tabs. But since Chrome is one of the worst browsers in terms of handling smaller tabs, let's just suppose that actually Chrome does not want users to push the New Tab button as much as it has in the past.
If Chrome makes it less instinctive to just keep banging that 'New Tab' button, then people will open fewer tab pages, show less tabs, encourage more re-use of tabs, and ultimately provide a simpler and better experience.
When you have one or two tabs open, the 'New Tab' button is by definition easier to see, quite discoverable, and easy to explore. When you have many tabs open, the button is less prominent and therefore less easy to be pressed instinctively.
And that's why I think the button is blank and anonymous - they just don't want you to use it so much - in case it makes you jump ship to another browser - like I did.
Internet Explorer 9 does not adorn its 'New Tab' button either, but they do show icon and tooltips on hover.