I'm glad you're paying attention. The summed price variable's standard error isn't on the same scale as the other part-worth coded attributes (for which we state the 0.05 or less rule of thumb). See further explanation below.
I have also observed that summed price has larger standard errors on that single coefficient (linear price) than the part-worth utilities where we employ effects-coding in the design matrix and where a beta is estimated for each attribute level. There are multiple causes for that, one being the fact that the summed price variable has a positive correlation with other part-worth parameters in the design matrix. But, the other cause (perhaps the biggest cause) is just due to the way we code the summed price variable in the design matrix (the magnitude of the actual values for price we place in the X matrix). This makes the standard errors not on the same magnitude scale between summed price and other attributes coded as part-worth.
So, as long as you are following the rule of thumb to vary summed price (the random shock) by around +30% to -30% of summed price, then you are going to be OK for the summed pricing variable (we have a white paper demonstrating that assertion using simulated data sets, if you are interested). Once you are on good footing there (enough independent variation in the summed price variable), I would then focus on the non-summed price attributes and follow our "0.05 or less" rule of thumb for assessing sample size considerations for ACBC. In short, you can ignore the fact that for summed price the standard error is larger; that's to be expected just due to the way we code the summed price variable in the design matrix.