Data Flow Transform Not Automatically Mapping Columns
Copying and pasting SSIS packages can lead to a few issues. It sounds like you have simple packages - a dataflow with a source to destination. Generally, those don't have the hangup I've run into but I have seen situations where people were inconsistent in their definition of data types. Email - varchar(40), varchar(80), varchar(120), nvarchar(256) all in the same database, just in different tables. What can happen is that you first build your package using the 80 size. When you copy/paste and fix your source table, the editor may not pick up on the data size change when you goto the 40 table because it fits within the old sizing. But I've also seen the reverse - it might not pick up the increased size. Resolution isn't horrific, just change your query to select 1 AS x, let it set the metadata and then fix your query back to the proper select.

As Dave suggested, this task is ideal for an entry level Biml task. In fact, as along as you don't mind not having your explicit source query, my Biml replicate-o-matic is pretty much exactly what you're describing. Earlier incarnation is on SO and I'm linking to it to hedge against link rot.

If you like your approach, you can keep your approach. But, save yourself the clicking and dragging in your destination and replace it with six clicks: three  right, three left. In your mappings tab, right click to bring up this context sensitive menu



Left click "Select All Mappings"

Right click and the left click "Delete Selected Mappings"

Right click and then Left click "Map Items by Matching Names"