Every time someone rolls a set of dice, it takes on average between 30 and 60 seconds to get a result. So, the more dice rolling you do, the longer the combat will take.
As a side note, there are plenty of videos on the Internet of real life combat. Both sword fighting and gun battles can easily be found. Now, pick a few and try to run those as combat with your $system. How long did that take?
So, you can speed things up by doing a little statistics. A normal distribution can give you a good spread of numbers: Just adjust the variance for more or less edge effects. Once you have this, get a few samples from the distribution. Combine these numbers with the mean (not the average) of the dice that the opposition rolls. Now, you have all your dice rolls results in about a minute.
Once you are going onwards on that path, it becomes easier and easier to just abstract the rules and just do what feels right. Suddenly, you are more a director in a movie than a chess player. You role play the combat instead of roll playing it -- bad pun intended.
Eventually, you can get rid of dice rolls completely and eventually get rid of the system entirely.
Note: Clearly this does not work if you like war game style combat systems.
Note on critical hits: The frequency of critical hits are over exaggerated in nearly all systems. Here's an exercise for the reader. Take a sample of MMA or Judo or boxing completions. Break said fights into "combat rounds" and statistics should tell you how many critical hits should have been scored according to $system. Then compare with how many critical hits were actually scored. But one can still account for critical: Given X samples from a distribution Y, what is the probability that number Z will come up? Now, you can model critical hits easily but I pity your party -- they will feel that pain! Statistics are great.