I would like to emphasize the distinction between pretending to actually be some other company or individual, as in phishing, versus just using the trademark name or something similar to a trademark name to cash in on the better reputation or more known name to sell your own stuff.
That first kind of nefarious activity is fraud and is covered under other laws so using trademark law is not necessary. For websites, like banks, that really need to be secure, there are technical solutions; use of HTTPS along with digital certificates and use of graphical site identifiers before supplying a password. This is really a more serious crime than just trademark infringement, so why use trademark infringement laws to fight it? Otherwise, you can be reduced to arguing over trivialities about how little a difference there can be in spelling a word before it represents trademark infringement. This is what I meant by saying relying on trademark law is a bad solution.

I am not arguing that trademark law should be abolished. However, it does have a particular problem on the internet. Trademark law allows two, or more, instances of the same name if the products or services are not in the same category, or categories, as specified during registration. On the internet, you don’t necessarily know until you arrive at the website what that URL represents. So who has priority on a domain name? Trademark law is not a sufficient solution to solve this problem. In this context, arguing over spelling differences seems especially trivial. Add in the amount of time wasted over things like Godzilla versus bagzilla (Sears) and Godzilla versus Davezilla (who didn’t even sell anything) and the whole issue starts to become absurd.
I would argue that adding specific TLD like .travel have the potential to help clear up trademark fights over the same word being used for different things. You can separate them with more TLD categories. I do have reservations about this apart from trademark issues. On the other hand, gTLDs will not help, because a generic TLD is not stuck in any sort of category. The trademark argument again either sort of expansion is that these companies will have to repeat their fights for each new TLD. This doesn’t make sense because the law cannot resolve all conflicts anyway and users simply don’t search using top level domains explicitly. They generally rely on .com or whatever Google returns for a keyword search. Adding more TLDs won’t make any difference.