It would be interesting to know how people are using their Roger devices in noise. As mentioned above, the adaptive gain is based on the assumption that the Roger signal has a better SNR than the HA mic. That assumption is not always true.
As distance to the sound source is the most important factor to improve SNR, it could be that the hearing aid has an advantage over a Roger Pen in some situations. E.g. if you are sitting at a table and are having a conversation with the person next to you, with the Pen in the middle of the table, the person next to you could be only 50 cm away from your HA, while the Pen maybe 100 cm from the person. The Pen would then be at a 6dB disadvantage.
A side note on the Pen is that over a certain noise level (can’t remember which by heart, but I think Nikita posted a nice cheat sheet somewhere) it will switch from omni to directional automatically. It does this on the assumption (all these assumptions, sigh) that the omni mode is no longer adding any benefit. Directional pick-up is in principle better than omni, but if the Pen is not pointing at the person you want to listen to it will not help you at all, rather the opposite.
In general, the louder the noise level, the closer the mic should be to the sound source. Directional mics and other tech will increase the useful distance, but only to an extent. In the end it’s your own hearing that will set the limit. In really loud noise the lapel mode is what you want to use. Then you would have the closest distance possible, plus the directional pick-up.