The big struggle with deep models is their thirst for data.
MNIST is considered a simple toy example, and it has 50k images spread across 10 classes.
ImageNet has 1m images spread across 1k samples.
One of the things that has made image recognition in the form of categorisation easier is that using a network pre-trained on ImageNet, and then finetuning it to your task actually works pretty well and requires far fewer images.
The struggle with doing something like license plate OCR is that it's unlikely that doing that you can transfer the learning from ImageNet to your target task.
So, in reality your struggle is going to be more around the data than the model. If you already had a system deployed that was getting data in and you were getting some feedback of when your model failed, then this problem would be easily solved, but if you're building from scratch this is going to be your biggest problem.
And since you don't necessarily know ahead of time how easy or hard your problem is, you don't know how many samples you will need or how much it will cost you.
So, if you did actually want to build a license plate reader using deep learning, my suggestion would be to try and artificially create a dataset by generating images that look like license plates and sticking them in photos in the state you expect to see them in (i.e. blurred, at weird angles, etc) and then training a neural net to recognise them. That would give you a sense for how hard the problem is, and how much data you will need to collect.
In terms of the model; I would probably just try having 6 outputs with 36 classes per output corresponding to the characters/digits in order. I don't know if it will work well, but it's a good baseline to start with before trying more complicated things like attention models or sequence decoders (https://github.com/farizrahman4u/seq2seq )