How do high-end restaurants promote such intense flavour in vegetables?
You actually answered your own question, it's the quality and freshness of the ingredients which makes the food in a great restaurant so good. A heritage variety beet which has been hand weeded and cared for before being picked at the optimal time and cooked within a day will be a totally different eating experience than an industrially grown variety that has been picked for volume and pesticide resistance, grown for size over flavor and then takes a week between being picked and appearing in the supermarket. 

Top chefs spend a great deal of time, effort and money sourcing the very best ingredients. Often the chef personally hand picks their ingredients, and some even control their own supply chain by having large gardens or even farms. Of course great chefs also are very good at preparation and flavor pairings, but with such simple dishes the ingredients have to stand up by themselves. 

In order to get high quality ingredients you need to find a source other than the supermarket. Supermarkets rely on volume, and the varieties they stock are chosen for volume and shelf life - they are all competing on price so the longer the food lasts and the more that can be grown for less money the better. You aren't going to find the most flavorful varieties in the supermarket, and they will have been picked before they are at their peak so they don't rot before they get on the shelf. Farmers markets, food co-ops and the like are often good sources for high quality vegetables. You can also go to the same markets the chefs do (depending on where you live). Not all suppliers will sell straight to the consumer, but some do. Just be prepared to get up at stupid o'clock and be prepared to open your wallet wider than usual - the best does not come cheap! If you live in the countryside another option would be to drive to farms in your area and see if you can buy direct. A farmer can sell you produce for half the price of the downstream supplier and still make more profit. 

Another option to get great vegetables is to grow them yourself, there's nothing better than a tomato picked straight from the plant and it's not hard to do. Growing your own is also incredibly cheap, you just have to be willing to put in a bit of time.