One could optimize test error over hyperparameters by various methods. But at that point does test or validation error continue to provide the functionality that a test or validation set is supposed to provide ?

You are not doing away with the test/validation set. You are doing away with:

   1. grid search - you would now only test for parameters that look promising (based on some criteria). Instead of covering the whole grid, you want to be smart about which points to try out. [1]
   2. you might still do grid search but you want to preferentially allocate resources to parameter exploration based on how promising they seem. Hyperband - [2]- is an example. 
   3. you can do both - you can be smart about picking parameters, but for the ones you pick you can preferentially allocate resources. Ex *Bayesian Optimization and Hyperband* (BOHB)

[1] Bayesian Optimization using Gaussian Processes is an example of this. https://arxiv.org/pdf/1206.2944.pdf Here's a library that helps you do this: https://github.com/JasperSnoek/spearmint. But there are other techniques in this family like Randomized Online Aggressive Racing (ROAR), Deep Network for Global Optimization (DNGO), Tree-Structured Parzen Estimators (TPE), etc

[2] Hyperband: https://arxiv.org/abs/1603.06560

[3] BOHB: https://arxiv.org/abs/1807.01774

Yeah that makes perfect sense -- optimizing hyperparameters more efficiently but on the train set.

Do you really consider this an obstacle? Obviously you need to have a validation set for the optimization and a new/unused test set for estimating out of sample performance.