There are a couple of arguments for
not using a tweeter. One is that you eliminate time alignment, phasing, and crossover issues pertaining to the relationship between the mid-range and the tweeter. Secondly, it makes for a more simple system, either eliminating a passive crossover or eliminating an active and a pair of amp channels.
That method was "standard" for years in cars as manufacturers tried to save money - speakers used "whizzer" cones.
There are some great "do it all" drivers out there...Fostex is one such brand that gets a lot of recognition for using that method of design.
To my ears, as neat as it is, it never sounds as good as a well-designed system with a tweeter added.
That is because it is a compromise - a mid-range simply cannot replicate highs as well as a tweeter can - and that is what this is all about - accurate sound replication.
In the end, however, it is your car - so if you are happy with a single driver for mids and highs, that is all that matters.
I would recommend that if you do go in that direction, consider something like this that is purpose-built as a full-range driver that will play the highs for you.
Fostex FE166En 6.5" full range: Madisound Speaker Store
8" if you are going totally custom:
Fostex FE206En 8" Full Range: Madisound Speaker Store
Another 6.5 - different design, same concept (this is what I would do if doing a full-range driver):
Fostex FE168EZ 6.5" Full Range Sigma Series: Madisound Speaker Store
Oh...and there is precedence in home audio circles for how great these things can sound:
Google Cain & Cain: