do you think there would be any problems?
Any problems?
For starters, there would still be things like hunger, poverty, and war in various places on earth. Even Jesus told Judas that they poor would always be with us. So, yes, despite registration of this domain name, there will continue to be problems.
It is, of course, impossible to talk about something without identifying the subject of the discussion. So, from that perspective, the use of a trademark in order to identify the subject matter of a discussion about the trademarked goods or services themselves is a perfectly acceptable nominative use. One needs to exercise care to avoid an impression that the owner of the trademark itself authorizes, endorses, or otherwise supports the discussion.
Does that mean that the trademark owner might not object? No. People make all sorts of claims all of the time. If dealing with an objection is a "problem", then, yes, if the trademark owner decides to raise an objection, then you would have one.