Better yet would be using one format of position.
Decimal degrees is far superior for integrating into software. And would be my first choice to standardize on. D-M-S is a pain to dump into any software, and usually has to be converted to decimal degrees anyhow.
Standardization sounds good in theory, but is probably impractical in practice. The problem is that other formats sometimes work better for various users and situations. If, for example, one wants to plot a position on a paper USGS topo map or nautical chart, decimal degrees are a real pain to use. Aircraft and nautical users frequently work in degrees and decimal minutes. Many land GPS users prefer to use UTM coordinates. For land SAR, the National SAR Committee recommends using the US National Grid (a UTM derivative, similar to the Military Grid Reference System). If you ask a reporting party to send coordinates in a system they don't normally use and are unfamiliar with, you risk having the coordinates corrupted at their end. Much better that they report in the system they are most comfortable with. Then make sure you capture that accurately, and pass it on to the SAR agency accurately.
The bottom line is that if you are going to get involved in SAR, you need to understand all these systems. When communicating, you must be sure you know which system is used. If necessary ask the reporting party. Then do a read back. Then double check that the communicated position makes sense. Also note that these days, most software packages can be set to take input in various formats. For example, SARTopo can use UTM, USNG, Degrees, Deg Min, or Deg Min Sec,
The key is to make sure you know which format is in use!