I have always spent more on the source compared to the amplifiers. My recommendation is to spend equal amounts on all components, and I am a firm believer in the weakest link concept of audio.
One thing is that the difference between a $1k and a $2k CDP may not be very much. They may even use the same parts. Notable differences in CDP occur at larger increments in price. There are some great sounding and outstanding values in CDPs under $2k. However, the jumps in quality are probably more in line at $5k, 7.5k, 10k, etc.
As your amp improves, you are likely to hear weaknesses in the chain, including the source. They may not be obvious in the first 30 days, but you may hear them over time.
The OP noted that a more expensive CDP had a slight improvement on A/B comparison. Sometimes, slight improvements can result in a large difference in enjoyment. The opposite may also be true, in that large and obvious differences may not translate into more enjoyment, despite clearly being an improvement. The question more relates to system goals and synergy, and creating a sound that draws you into the music and not into the sound itself.
Another consideration is the type of music. Good CD players excel at unamplified acoustic instruments that have a natural resonance, placed upon a stage of a certain width, depth, and height. Not all music is recorded in this manner with regards to rock, popular, and electronic music. Even acoustic jazz in the 50's and 60's had been engineered to have an unnatural presentation, with exaggerated stereo separation, close miking, filters, and an inflated image size. It takes time for your ears to open to these new details. An inexpensive CDP can convey the brushes on a cymbal or the fingers sliding up and down a fingerboard of a guitar, but they may not convey the spatial details of the performance. The point being that some musical genres may benefit more from money spent on amplification. If you like rock, then yes, the speaker and amplifier are going to be much more appreciated.
One thing is that the difference between a $1k and a $2k CDP may not be very much. They may even use the same parts. Notable differences in CDP occur at larger increments in price. There are some great sounding and outstanding values in CDPs under $2k. However, the jumps in quality are probably more in line at $5k, 7.5k, 10k, etc.
As your amp improves, you are likely to hear weaknesses in the chain, including the source. They may not be obvious in the first 30 days, but you may hear them over time.
The OP noted that a more expensive CDP had a slight improvement on A/B comparison. Sometimes, slight improvements can result in a large difference in enjoyment. The opposite may also be true, in that large and obvious differences may not translate into more enjoyment, despite clearly being an improvement. The question more relates to system goals and synergy, and creating a sound that draws you into the music and not into the sound itself.
Another consideration is the type of music. Good CD players excel at unamplified acoustic instruments that have a natural resonance, placed upon a stage of a certain width, depth, and height. Not all music is recorded in this manner with regards to rock, popular, and electronic music. Even acoustic jazz in the 50's and 60's had been engineered to have an unnatural presentation, with exaggerated stereo separation, close miking, filters, and an inflated image size. It takes time for your ears to open to these new details. An inexpensive CDP can convey the brushes on a cymbal or the fingers sliding up and down a fingerboard of a guitar, but they may not convey the spatial details of the performance. The point being that some musical genres may benefit more from money spent on amplification. If you like rock, then yes, the speaker and amplifier are going to be much more appreciated.