It is unwise to rely on the etymology of a word to discern its meaning, or, if it has a range of meanings, to insist that the "original" meaning is somehow "more correct" . Words mean what they mean. In any discussion of the meaning of a word it is often instructive to look at its etymology as a starting point, but once you have done that you have to move on.
The problem with defining a consonant as a sound that cannot stand on its own is that you then need to go on and ask: "If it cannot stand on its own what does it have to go with?" and the answer to that will be "a vowel". So you then ask: "What is a vowel?" If your answer to that is "any sound that is not a consonant" we end up with consonant being defined in terms of vowels and vowels in terms of consonants, which is not very helpful. That means you need to define one or the other in its own terms and without reference to the other.
If we decide we shall start with defining a vowel, a reasonable enough definition is one that says it is a sound that is made without any obstruction of the vocal tract. When we have done that we have to decide what sounds in the language we are looking at are vowels. When it comes to the sound /w/ we may have some difficulty in deciding. The tricky bit is (because at school we were taught that the vowels are
a e i o u) that at the back of our mind is the idea that /w/ ought to be a consonant and it is difficult to overcome it. This partly arises out the failure to distinguish between the sound /w/ and the symbol <w>. If the difficulties can be overcome, it is not totally unreasonable to come to the conclusion that /w/ is nothing but a short /u/. The articulation of /w/ does not seem to involve any obstruction of the vocal tract. If we move on and look at the contexts in which /w/ is found it is not unreasonable to conclude that it is never articulated on its own, or, as you put it "you cannot pronounce W without attaching a vowel to it." However (forgetting for a moment that we have not yet defined consonant) that does not justify us calling /w/ a consonant if we agree that its articulation does not involve any obstruction of the vocal tract. It is perhaps more apt to call /w/ a non-syllabic vowel - our definition of vowel does not imply that it must be capable of forming a syllable.
If we decide to start with defining a consonant as a sound that involves some obstruction of the vocal tract, I think we are going to come to the same difficulty when we get to /w/. [It would be tedious to set the process out as in the previous paragraph.]
The fact that in the IPA there are separate symbols /u/ and /w/ says something. I am not quite sure what it says, but the possibilities are:
1. There is a qualitative difference between the two
2. There is a quantitative difference between the two and it is useful to be able to indicate when the sound is syllabic and when it is not
3. The whole thing is confusion
It may be noted that any two phoneticians may disagree about whether a particular utterance should be transcribed using /u/ or /w/. To an extent the convention for a particular language may depend on whether that language has a separate symbol for /w/.
The fact that many languages have the sound /w/ but have no symbol <w> to represent it (instead using <u>) also says something. It says that the way that any language is written (if written with an alphabet) involves a prior analysis of its sounds. When we come to look at the language afresh we must not be unduly influenced by that prior analysis.
The questions raised by this thread arise partly because written English employs an alphabet. Apart from the fact that that leads to a confusion between sound and symbol, in an alphabetic system language is analysed into phonemes. That is fine as it means that only a relatively few symbols need to be employed and the success of alphabetic systems throughout the world speaks for itself. However, the analysis of speech into phonemes is artificial (though it does not seem so because of the way we write!) and the natural division of continuous speech is the syllable.