The biggest issue is that neither you nor your employer can just decide one day to move you to 1099. It sounds like your current job means you come into an office everyday at a time dictated by your employer, use company equipment to do your job, have a set yearly salary, and have no other clients. While there are some gray areas to 1099 to W2, it seems clear that in the current incarnation of your job you are an employee.
All that said, *if* you could convince them to do 1099, I don't think anyone would actually care. The IRS only seems to get involved in 1099 disputes when an employee says they're misclassified. But if I was the employer I would not do this as in a year or 2 there's nothing to stop you from saying I was trying to screw you.