Myofascial trigger points — muscle knots — are a ubiquitous muscular dysfunction, causing most of the aches, pains and stiffness in the world, and complicating virtually every other injury and disease process. A lot of massage is focused on them, directly or indirectly. Massage may be helpful because it relieves the symptoms of muscle knots, or even unties them. (No, not literally.)
The significant benefits of Swedish Massage make it clear that a regular massage regimen is more than a luxury, but indeed an important ingredient in the cultivation of physical and emotional well-being.  Maybe you just want a “relaxation” massage.  But know, that in your relaxation, you are also taking care of both your body and mind in fundamental yet important ways.  
There’s just no reason to push a client to that “cringe point.” It’s ham-handed, tends to indicate a simplistic “more is better” approach to the work, and simply isn’t needed — that’s not what defines “intensity” in a good massage. Very strong and sastisfying pressure can always be achieved without that edgy, nervous-system-almost-rebelling feeling.
There’s rarely any justification for extremely painful massage, unless it clearly produces a better result than gentler treatment — which is rarely clear!1 It is possible that a few “brutal” deep tissue massages could do the trick where gentler treatment would fail — but there is no way to know this in advance, and massage is expensive stuff. If you’re going to gamble on a treatment, gamble on cheaper and less painful ones.
One narrative review in Open Access Journal of Sports Medicine explains that the impact of using these two modalities combined are somewhat inconclusive, mainly due to research limitations; however, after looking at 21 randomized controlled trials, the author ultimately concluded that “the effects of cold and static compression are clearly better than no treatment.”

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