Does anyone use a faucet attached water filter in the shaving den?

I'm thinking about getting a filter to attach to the bathroom sink faucet. Reviews of such products are mediocre so I have some concern about the efficacy of these products. Do any of you use one and can share your thoughts on it?

I'm thinking something like this: https://www.amazon.com/dp/B005A3WRA8/?tag=adhs-20

The FIRST thing I would do is check how much replacement filters are and how often you need to replace them if I were to buy one.

Yes. I’ve don it with a really good filter from Amazon that I use in several rooms. It takes some “do it yourself skills to make the proper connections/adapters, but I’ve been very happy with them.
https://www.amazon.com/dp/B000E77I0Y?ref=yo_pop_ma_swf

I haven't done this. Here are some questions I would ask myself if thinking about this:

1. Is there a problem or concern I need to address? What do I want to achieve? i.e hard water, contaminated water, etc...
2. How is the water quality where I live? I don't drink a lot of water from the bathroom tap, though I do drink a little.
3. Does the unit I'm considering allow hot water to be run through it? I have a different brand on my kitchen faucet. It specifically says in the instructions to only use cold water and never hot.

All good points. Mine is only connected to the cold water supply. Since warm water is made up of mostly cold water with a little bit of hot added, I find it an effective way to reduce the amount of calcium and other hard minerals in my water. Does it have a noticeable effect on my lather? I dunno, but it makes me feel better.

In my mind, that fact that it makes you feel better is a great reason to have one.

You mention lather quality in your post with brings up a good point and causes me to think about Mitchell's Wool Fat. We all know that it is a great soap. Many of us, who are experienced and know how to make lather, can't get good lather from it. I've been wondering why that is. Differences in water may be part of it. If there is something in water that binds with something in MWF, then it may cause problems.

There is no question that some soaps don’t like hard water. That’s originally why I put in the filter. I don’t know if MWF is one of those soaps or not.

I installed a water softener. To be honest I haven't noticed much effect on my lather. And I am on a well. Very hard water previously.

I just added a tankless hot water heater and they recommended a quality filtration system before the water reaches the hot water heater and one on the cold water line. Honestly I have not seen any difference in lather and I have a den full of all types of soaps.

Now I do feel the difference in the water and the taste of the water is so much better.

I installed a water softener.  To be honest I haven't noticed much effect on my lather.  And I am on a well.  Very hard water previously.

Thats interesting, I've had a water softener for years and I find my lather to be quite good with the exception of B&M Reserve soaps and Mystic Waters - those give me trouble although I've never given them a run with hard water to see if its the water or just me. I recently was on the road for a while in Northern Ontario. I think the water was moderately hard. I was using a Tabac soap stick with a fairly small knot - Simpson's The Major travelling brush. I was able to lather reasonably well but what I did notice was the almost immediate buildup of soap scum on the razor - Rockwell 6s. I don't get anything like that with my softened water and what little buildup that does occur takes a long time. Its all part of the adventure I guess.