Alternative-specific designs indeed are different from just setting prohibitions.

For example, consider two attributes each with 3 levels.

Brands: A, B, C
Colors: Red, Green, Blue

And, imagine that you want to prohibit two of the combinations from occurring (Brand A can ONLY show with Red).

If you were to try to use a standard CBC design to create those two prohibitions between Brand and Color, then the software would code both attributes for main effects estimation. In other words, it would estimate the 3 levels of Brand and the 3 levels of Color. Meaning, it will try to estimate the effect of each attribute independent of the other attribute(s). But, due to your prohibition, there would be correlation in the design matrix (columns for brands would have non-zero and relatively strong correlation with columns for color).

The type of coding that is used behind the scenes during this estimation is effects-coding, where in reality K-1 betas are estimated for a K-level attribute. So, in actuality (3-1)+(3-1)=4 total parameters would be estimated. Due to the correlation introduced by the prohibitions, these betas would have lower precision than if no prohibitions were in place.

Now, let's consider what would happen under alternative-specific coding. Now, there are three attributes in the study:

Attribute 1: Brands: (A plus hard return plus Red), B, and C
Attribute 2: Colors for Brand B: Red, Green, Blue
Attribute 3: Colors for Brand C: Red, Green, Blue

With alt-specific designs, attribute 2 levels only appear in concepts when attribute 1 is B. Attribute 3 levels only appear in concepts when attribute 1 is C. There is zero correlation between the three attributes in the design matrix.

Let's count up how many parameters are estimated:

Attribute 1: 3-1 = 2
Attribute 2: 3-1 = 2
Attribute 3: 3-1 = 2

for a total of 6 parameters estimated rather than 4 with the standard design plus prohibitions. So, the alternative-specific design is a bit more expensive to run (has to estimate a few more parameters given the same number of respondents and choice tasks as the standard design with prohibitions). But, the counterbalancing virtues are that the design is orthogonal (zero correlation between attributes), which usually leads to more precise parameters compared to designs with bad prohibitions, and also if there is an interaction between brands and prices, you will be capturing that interaction with the alt-specific design. (The alt-specific design estimates two separate color attributes, each with respect to how the three levels of color are valued when combined with brands B or C.)

why alternative specific design is better than prohibitions?