My staff will not be able to figure out a new tool. They are used to going straight from copy selection in Arc to pasting directly into Excel. Right now they are all using Arc 10.5 and Office 2010 (I'm the only one with an earlier version of Office).
One thing I did forget to mention yesterday (too many pans of the fire) is that if you do a sort (on any field) before doing the copy paste the correct number of records show up in Excel. The response I got back from tech-support this morning is below (hasn't sent me the bug number yet).
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I did some more testing on the data though and believe that the issue may be with Excel. I will outline the testing I did below.
1. Tested copying the records into Excel with no joins or relates from the shapefile- Success
2. Imported the shapefile into the geodatabase as a feature class and did the same test- Success
3. Exported the table of the 8358 records and joined it to both the shapefile and feature class- Success
4. Related the exported table to the shapefile as well as the feature class- Reproduced issue only with related feature class.
5. Copied the same clipboard of records to Notepad ++ and all 8358 records came across. Excel still showed ~2050.
6. Cleared related tables and tried relating again to feature class- Success, issue did not appear second time
7. Attempted multiple times to reproduce the issue and re-added datasets each time to new map without success
Results above were tested with ArcMap 10.4.1 and Microsoft Office 2016.
At this point I have been able to reproduce the issue once and it was specifically with a feature class that had a related table. However, this was not consistently reproducible and when pasting those same exact records into another text editor they all loaded fine. This may be attributed to having an older version of Excel, but the oldest version we can test with is 2010. That being said, my next step will be to test ArcMap 10.5 with Microsoft Office 2010 since it is the closest I can get to your machine.
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I did run his step 5 (with both Arc 10.2/Excel 2007 and Arc 10.5/Excel 2010) on Feature Classes without related tables in 2 different file GeoDatabases on both Notepad ++ and Excel came up with the approximately 2050 records.