Your question can't be answered without knowing where you live. For example, shipping a desktop PC from Europe to the USA will cost a fortune as well (for private persons).
Furthermore, you should think about what happens when the PC becomes defective: You then would either have to make the colocation company ship the PC back to you, then you would have to repair it and send it back again, or you would have to make the colocation company repair your PC. Both variants will cost a lot, and (probably much worse) will make your PC unusable at least during the shipping time / repair time.
And what happens if your costly PC gets damaged during shipping? Be prepared to pay high shipping insurance fees, and be prepared for a lot of hassle, if not a litigation, if something bad happens.
Let alone the problems when you PC gets stuck at the customs ...
Finally, nearly each company which provides colocation requires the PCs to be in rack cases (19") (at least, the last offer to colocate standard case PCs I personally saw was about 15 years ago ...). Commonly, colocation cost will scale linearly with the number of HUs (height units) your PC takes in the rack.
Therefore, I'd like to propose another solution: Buy a solid router which has common VPN techniques integrated, and place it in your home where your desktop PC is. Buy a reasonable laptop and take it with you everywhere, end establish a VPN from your laptop to that router whenever needed. Using the VPN, operate your desktop PC via Remote Desktop (if it runs Windows) or similar techniques (if it runs another O/S).