Diaglosia – the inherent ability to switch from an accent, is an inherent part of the Indian Culture. The real skill, if one is interested, is in switching from one accent to another if need be (fun with langauge) and come back to your own space. The skill stops flowing if you get married to a perceived American/British/Australian or Timbuktoo accent, and not have the ability to come back. Just imagine if you can say “Howr u doin?” but cannot say “How are you doing?” Thats another burden to carry.
Also, you are who your voice is. If there is staccato in your voice, then the same staccato comes in your daily activities, for sure.
Like everyone mentions, the key is to be yourself and not more American than Americans.