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Pinching is normally done on much younger and smaller plants to encourage bushing out. It should not hurt the plant either way, however, so if you would like to pinch them back, go ahead.

Here is a link to help you.

https://www.gardeningknowhow.com/edible/vegetables/beans/get-bean-plants-to-bloom.htm

Here is an article that will help you that discusses why bean plants do not bloom:

https://www.gardeningknowhow.com/edible/vegetables/beans/get-bean-plants-to-bloom.htm

Happy gardening!

Beans will stop production in really warm weather. Also, beans will stop producing if seeds were allowed to form inside the pods, so it is always recommended to regularly pick your beans (which I believe you did). Extremes in soil moisture can also halt production. Plants growing in soil that is too wet or too dry are stressed by a lack of oxygen and water.

It sounds like you have too much nitrogen in the soil. This will make for a large, lovely plant with no flowers, thus, no beans. Try adding some phosphorous to the soil to help balance it back out. Bone meal is a good source of phosphorous. If you are seeing blossoms but no beans, this article should help: https://www.gardeningknowhow.com/edible/vegetables/beans/bean-blossoms-no-pods.htm

Well-drained soil, a support system and plenty of mulch are key to healthy Pole Bean plants. Make sure they're getting full sun if possible. They also need to be kept off the ground at a very early stage. With all of these situations correctly balanced, you should have a full harvest of Pole Beans within 60 to 70 days. This article may help you:
https://www.gardeningknowhow.com/edible/vegetables/beans/growing-pole-beans.htm