Should you wait certain amount of time after steak reaches 170 degrees internal temperature

The first question I would ask yourself is, why do you want your steak to be 170 degrees? The temperature and "well done" is just an arbitrary measurement and you really should look deeper to get a better answer. I see a few potential answers to that question.

1 - You are worried about getting sick from under cooked food

If this is the case, you really don't need to be as worried about steak. But, if you are still worried, cooking longer never hurts to kill more stuff. The problem is you will find your steaks to generally by dry and not very flavorful (or maybe too flavorful if you get burn it). Cooking the steak slowly (at a lower temperature) will help to keep the steak a little juice while getting it to be well done. You might also want to get over being scared of getting sick and move on to option 2.

2 - You don't like steaks that still show some pink

If this is the case, then maybe some experimentation is needed. Cut your steak once it hit 170 degrees. If you don't like the look, leave it on a bit and know that in the future you need to let the steak sit for a bit longer. If you like the look, then take it off. After a few times of repeating this process, you will learn what you like. Remember the end goal is to get a steak cooked how you want, not reaching a specific temperature.

You will get to the point that you no longer need to cut your steaks to check them. You should also keep in mind that steaks will cook for a bit longer after removing them from heat. You may end up with a slightly pink steak during this trial and error process, just use it as a learning experience.

3 - You pride yourself in being able to grill, but you received a request from a friend for a well done steak

In this case, you don't have the ability to perform experimentation over time and may very well be scared to cut a steak before serving it to some one. Get over yourself and be willing to tell your friend that you are inexperienced with well done steaks and ask for some help telling when it is done. They may not be experienced themselves and will end up just cutting the steak to see where it is at anyways.

It will continue cooking for a few minutes because of the residual heat. If your end goal is 170 degrees, you would want to take it out earlier. I'm not sure of the exact conversion as I'm a medium-rare to rare type myself, but try taking it out around 160 degrees, then check the temp after about 10 minutes and adjust accordingly for future steaks and thicknesses.

You could practice the feel of the meat at each level of doneness during these learning curve steaks, too, and by the time you get the temperature estimating down you'll probably have a pretty good feel for medium, medium-well and well-done.

Yes and no.

No, because the process of cooking is not completed the second the meat reaches a certain temperature. If a certain protein denatures at X degrees, not all points of the steak will reach X degrees at the exactly same second as the tip of your probe, a few will need just a little bit more energy to change their structure, and so on. And then there is the resting process which occurs during the first few minutes of cooling, and during which the proteins relax again a little bit and soak up some juice back in.

But for practical purposes, yes, remove it from the heat the second it reaches the temperature indicated in the cooking table. That's because the temperature there was calculated to be the temperature at which you remove it for the best taste, not the exact point of some chemical change in the protein structure.

If you are using a food safety table instead of a cooking table, you can still remove the steak at the temperature reached, for exactly the same reason. It is indeed possible to kill the same amount of bacteria by either reaching X degrees or by reaching X-5 degrees and holding the food at that temperature for Y minutes. But the temperature in the tables is the one for instant-kill temperatures, not the one for "will kill them eventually" temperatures, unless you are using specialized tables like the ones for sous vide (which will contain both a temperature and a time period).

The above assumes that you don't want to overcook your steak, taking it up to the next doneness level. In your special case, there won't be any change, positive or negative, if you let it stay at 170 or higher, it just can't (over-)cook any more. Still, there is no need for letting it sit there. For any other level of doneness, you not only don't gain anything by leaving it on the heat, you even risk overheating.

You gain nothing by cooking any meat or poultry past its doneness point. Cooking meat well is about adding as little heat as possible to achieve the desired internal temperature in order to preserve its juiciness. Heat penetrates from the outside in, and the middle won't stop cooking until the inside and outside of the meat achieves temperature equilibrium, so as @MargeGunderson says you need to remove it from the heat before it reaches its doneness temperature. How much lower depends on the thickness of the cut and the type of cut. In a roast I'd say take it out 15 degrees lower, thick steaks 7-8 degrees F lower, and thin steaks 5 degrees F lower, but that's just estimates.