Amosu,
I agree with all the cautions already presented here. I have completed this customization for many customers - but the deciding factors to proceed were that they did not have any differences in their categories, workflows, or service levels between the types.
Simply changing the type after it has been saved does not automatically invoke any process that would be associated with that type. You must capture that change and then create all the necessary triggers, events, logs, etc. This can become unmanageable quickly.
The supported process here is for users of Self-service to create Requests only and then an analyst to create a new Incident from a Request using the original as the basis when required. This will copy selected fields into the new ticket and create a relationship between them.
You would then complete the Incident and then close the initial Request. The allows for separate processes for Requests and Incidents at the cost of possible confusing the customer with two tickets.
There is not, however, a 'Create Request' from the Incident form. (There was an Idea for this as some point in the past).
If you enable both Requests and Incidents from Self-Service, then I recommend you take efforts to make the distinction clear to the users. Here is a sample I helped one customer to develop:
Good luck!
J.W.