Complex is no reason not to do it. Tobacco was complex when they were throwing money at sports sponsorship and everything else they could think of but a way was found to do it. Even though it might be difficult to distinguish in legal terms between a gourmet restaurant and a junk food craphole, anyone with common sense can immediately see the difference. It is just a matter of will. When enough people get past the short-term pleasures and the vested interests and start to take the damage seriously, things will suddenly become a lot less complex.
I agree that unhealthy food is readily identifiable. But common sense has no value in tax law. It's about legally defensible tests. You need to be able to clearly identify something and tax it. Tobacco and alcohol taxes are comparatively simple: Entire categories are taxed and there are small number of subcategories. Booze is taxed per volume. Tobacco may be taxed per weight (I'm not sure). It's simple and the manufacturer/importer pays.
You can get unhealthy food at a gourmet restaurant. lots of luxury foods are unhealthy. I was most overweight when travelling frequently for work and eating at restaurants often. Subway and sushi saved me more than my running shoes did
Food gets very complex, very fast. Complexity is really about time and cost. Perhaps impractical is better word. Either way it's a legitimate reason not to do something. For example the cost to administer such a scheme may exceed the identifiable cost to the health system of obesity. Then there is the risk issue of displacing consumption away from commercial to home-made - tax ingredients too?
I think you will also find that poorer households are hit harder by such a tax. Wealthier people can afford luxury food that is also healthy.