You include the helpful note that your garden gets a lot of shade in the morning and afternoon. Few vegetables like shade. In general, the stronger a plant is, the more likely it is to fare well despite the “common cold” varieties of insects and diseases with which every plant lives. If the shrubs and creeper are what is heavily shading your garden then yes, it is likely they indirectly are enhancing the insect infestations. In that case, though, likely so is the fence underneath or behind them.
Beyond that, the insects are unlikely to be affected much by the surrounding plants. Grasshoppers do thrive and shelter in tall unmown grass, particularly wheat. That doesn't look relevant to your yard.
All three unwelcome residents, aphids, caterpillars, and locusts / grasshoppers, share several characteristics. First, each is widespread and common, nearly worldwide. That means there almost certainly are background populations nearby and every year. The neighboring insects will tend to replace those that you kill. Second, there are at least thousands (!) of species of each, most of which are host-specific. That is, each kind seeks out only one or a few species of plants. (Major outbreaks of grasshoppers are an exception.) So even if one species thrives on a garden plant or an ornamental and may occasionally overflow onto the other, the populations on the two plant species are unlikely to be mutually reinforcing.
Another characteristic the three groups of insects have in common is that their populations tend to fluctuate a lot year to year, mostly in response to fine variations in weather. For example, cold, wet weather in the few days immediately after spring egg hatch is very destructive to tiny new grasshoppers. The differences you see between your current and previous gardens may be due in part to different weather in various years, as well as potentially other subtle environmental differences between the locations.
Aphids (and to a lesser extent caterpillars) are particularly defenseless. They reproduce at a breathtaking rate. Generically that means that their populations are controlled by high rates of mortality, not by limited numbers of mature parent individuals. Perhaps you may want to focus on enhancing their natural enemies rather than killing some of the individuals while the rest continue to multiply. For aphids, enemies include lacewings, lady beetles, and numerous species of (to humans, stingless) parasitic wasps. While a few insecticides are specific to orders of insects, others aren’t. It’s possible spraying is helping, and it’s also possible it’s hurting the campaign to reduce the numbers of pest insects. Also, aphids will ebb and flow on their own. That is because they do best when it is relatively cool, in your climate spring and fall but less so in high summer.
To reply directly to your question, except to the extent that the shrubs weaken your vegetables by shading them excessively, removing adjacent ornamentals isn’t likely to help.
