running workouts faster than prescribed - smart or stupid?

Depends. Is the coach aware that you exist?

If it's a good coach and they know you, then you are being stupid. You should get more benefit from following the plan and trusting the process. This should become apparent when you can't hit workout targets because of fatigue.

If the coach doesn't make the plan specifically for you, then they could be aimlessly generating target out of their butt, in which case what you are suggesting makes more sense.

If you just started working with a new coach, then maybe they haven't figured you out yet, but it would be better to ease you into training than to kill you right away. In the end, if it's a good coach and you communicate, then they should have you doing what's best for you shortly.

When you run workouts a lot faster than goal pace, your energy system switches from aerobic to anaerobic. In other words, you are NO LONGER training your aerobic system, which is where the overwhelming majority of your training should be as a distance runner. Instead, you are training your anaerobic system.

The anaerobic system can improve rapidly, but it has a relatively low ceiling to improve. Once you reach that point, improvement stops. The aerobic system improves more slowly, but it has a higher relative ceiling for improvement. It can improve for months or even years.

Running faster than goal pace prevents you from getting the optimal benefit to your aerobic system from the workout. It also takes more time to recover from a hard anaerobic workout so you are hindering your recovery day. If you run your recovery day normally after a hard workout that should have been aerobic but you turned into anaerobic, the lack of recovery will turn your easy day into a moderately hard day. Thus, you won't be able to put out your best effort in your next hard day.

You are sabotaging your training by running a lot faster than goal pace for the workout. As your fitness improves, as determined by races or time trials, you can increase your goal workout pace accordingly.

If you want to doublecheck your coach, buy a copy of Daniels Running Formula, 3rd Edition by Jack Daniels. Check out the tables that show what paces you should be running for various interval workouts at your current level of fitness

Race performances are the best indicator as to how fast workouts should be designed, and this means in order to train faster you need to prove you deserve to do that based on a recent race performance.

+1 I will add that the harder you run your workouts, the longer it takes to recover. So consider what is next on your schedule. If you have other workouts or hard efforts, you will be going into them less fresh than if you hit the prescribed paces.

Always run the purpose of the workout. Going too fast ruins it.

Every day ask yourself what's the purpose of this run and stay within that purpose. Even on easy days, recovery days, long runs, tempo runs, etc etc

Yeah, a very HS approach to hitting every workout as hard as you can. Sure will you will benefit, but you will not get the MOST benefits.

You could go to the track and do 10x200m hard as you can every day and get some benefit, but it will not be optimal.