The asset bits are there because those are the main types the group operates and thus if you have one or more of them then you are further up in the list with regard to immediate suitability as a new hire. If you do not have one of those types then you will need to be trained up in one of them at company cost.
Simply converting you is also not necessarily a win for the company either, as the clients (oil companies) dictate minimum requirements on type to qualify to tender a contract, thus your new conversion is still not a useable asset to the company without a certain number of hours under your belt.
Then there is the national pilot issue in whatever country we operate in. Quite often that is a condition of simply being allowed into the country and getting an AOC irrespective of whether the nationals are capable or not.