I don't know about the CRTs being better than LCDs. Rear Projection CRTs that don't have a shadow mask fit your description, but direct view CRTs will have their pixel sizes set somewhat by the shadow masks or vertical masks in the case of Sony.
If you are going to get a 1080p display, you will not be getting a CRT anyway.
The issue with poor SD is one of the sources. Digital sources such as cable and satellite have decompresstion artifacts that are magnified by the HDTVs. Some receivers handle them better than others and is worth trying to get a look at SD if possible before buying the TV or the source box. Here is an example of a decompression artifact:
The example on the left shows what is the most common decompression artifact. The other disappointment will be once you watch much HD it is hard to go back to SD.