This topic has made me curious and I want to throw my two cents in. I personally believe that fangames are a grey morality area.
I believe that fangames and modding don't really hurt companies financially, some companies such as Bethesda even encourage people to mod their own stuff as long as they don't break any copyright infringement laws. Fangames often cater to a certain proportion of fans that aren't being catered to by the companies themselves, whether going for a more mature (darker) story or increased difficulty/ creativity. The only time that difficulty is ever created in main series pokemon games is either through online competitive battling or via extreme level jumps like Dark Rising (Necrozma and Cynthia from Diamond and Pearl comes to mind here). Most people who play fangames are just looking for something outside the norm and will still buy the main series games to support the original company. Fangames also appeal to those who would never play main series pokemon in a million years but something about said that appeals to them so wouldn't hurt the company either way.
In regards to money, I think that fangame devs shouldn't actively keep pestering people for money (I don't see no fangame creators on here doing this but there probably are some out there that do) but if fans should wish to give donations then by no means am I against that as it's their choice. If a fangame dev does appear to hassle people for money then I agree that the fangame in question should be C&D'd. The mobile apps you often see on play store or app store that charge users to play and add microtransactions are definitely wrong and should be shut down as this causes way more harm than most fangames ever could.
Lets talk legal talk. Whilst I adore fangames myself and will never stop playing them, I agree with Commander in that fangames should not come under legal protection. Fangames themselves do use resources that was originally from GF themselves. The company is not obligated to allow them to keep running but probably will if they don't have too much presence (like Uranium sadly was). Romhacks fall more under piracy laws as it requires a base game to run.
Fangames could potentially benefit big companies if they choose to utilize them correctly. Let's say Game Freak did stumble upon Reborn and Rejuvenation and instead of a C&A, they decide to play through it in order to analyse what a select part of their audience may want? They could think "Hey, the sort of story may not be possible for our games but we could expand the field effects concept a bit more and increase our difficulty slightly if we had a certain mode" and then implement the ideas they got from these fangames. This could allow existing customers of their main franchise to be more satisfied and potentially draw more in.
I'm probably being a little naive in some areas but I'm going to sum up my opinion: Although fangames shouldn't be protected legally, they could be tolerated companies if fangames remain free (this is my morally grey self coming out here). Paid fanworks are bad and should immediately be C&D'd. Fangames will exist as long as companies only cater to a small portion of their true audience (not their perceived audience).