Not necessarily true. The OPs budget is 2k, so let's say pairing a 2k speaker with a 1k amp. There are 2k standmounts that are more demanding of amps. The KEF Concerto Meta is just above 1k yet is demanding.  Floorstanders at 2k would be more forgiving I concede.
The new Arcams the OP suggested are great components in their own right, but a 2k speaker is going to ask more questions from the 50w A5+ amp, that I guarantee you. And the amp ultimately will be room size dependent, because it's going to dictate the speaker.. New speakers today are shotgun pairings with amps. 6 and 4ohm nominal are becoming the norm, replacing the 8ohm norm.
In summary, do not indulge in the speaker and then skimp on the amp, that's just a fool's errand.