I think it's a terrific option for somebody needing to do a whole platform upgrade, but you don't need to, and that R5 3600 is definitely not as good, or as cheap, of an option as the 9700k would be since you would need both a CPU and a motherboard.. And you would not have as good of performance as with the 9700k. If you had an older platform and you already needed to get a new CPU and motherboard, then yes, it would be well worth considering because it's a very good all around CPU for the price, but one of those and a motherboard is going to cost you more than the 9700k will by itself.
PCPartPicker Part List
CPU: AMD Ryzen 5 3600 3.6 GHz 6-Core Processor ($194.00 @ Amazon)
Motherboard: MSI B450 TOMAHAWK MAX ATX AM4 Motherboard ($114.99 @ B&H)
Total: $308.99
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2019-11-28 03:55 EST-0500
or
PCPartPicker Part List
CPU: Intel Core i7-9700K 3.6 GHz 8-Core Processor ($299.99 @ Best Buy)
Total: $299.99
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2019-11-28 03:56 EST-0500
And the 9700k is going to give you much better performance, especially in gaming. If the Ryzen was the better choice, I'd say so, because I have no preference against AMD. The Ryzen 3000 series is a game changer when it comes to them being competitive or even in some cases better, than Intel, but in this case it's just not the best option.
If you look at the gaming benchmarks at the following link you will see that the 8700k beats the 3600 and 3700x in most of them, and the 9700k is better than the 8700k 90% of the time. There are only a few games, which are highly optimized for multithreaded performance, where the 8700k's extra hyperthreads wins out over the 9700k, and in those kinds of games the 3600, 3600x and 3700x are likely going to have a better showing as well but for most games, any CPU with 6-8 strong cores is going to do better than one with a bunch of hyperthreads.
Now if you were talking about doing the 3700x and a new board, that might be a different story. Then, selling your current board and CPU might look like a good option and moving up to those parts instead of just adding a CPU.