[TensorFlow] Why does the feed's shape matter in TensorFlow Grappler?

Before explaining this, you should understand what Shapes and dynamic dimensions are in TensorFlow. This article below explains the concept very well.
https://blog.metaflow.fr/shapes-and-dynamic-dimensions-in-tensorflow-7b1fe79be363
The key idea is:

• The static shape is a tuple or a list.
• The dynamic shape is itself a tensor describing the shape of the original tensor

Then, you need to add some debug information in the function: MetaOptimizer::OptimizeGraph() in the following file:
tensorflow/core/grappler/optimizers/meta_optimizer.cc

 Status MetaOptimizer::OptimizeGraph(Cluster* cluster, const GrapplerItem& item,
                                     GraphDef* optimized_graph) {
    for (const auto& f : item.feed) {
    const auto& shape = f.second.shape();
    VLOG(2) << "...[DEBUG] in OptimizeGraph(), input name:" << f.first
    << ", shape=" << shape.DebugString();
 }

After that, define your input shape of your model for 2 cases:
Case 1: Give a static shape with "None" for the batch size.
Case 2: Give a static shape with a specific value for the batch size.

tf.placeholder(self.image_dtype, [self.batch_size, self.image_shape, self.image_shape, 3], 'input'),
tf.placeholder(tf.int32, [self.batch_size], 'label')]

For Case 1, the debug information will be like this:

tensorflow/core/grappler/optimizers/meta_optimizer.cc:202] ...[DEBUG] in OptimizeGraph(), input name:input, shape=[1,224,224,3]
tensorflow/core/grappler/optimizers/meta_optimizer.cc:202] ...[DEBUG] in OptimizeGraph(), input name:label, shape=[1]

For Case 2, the debug information will be like this:

tensorflow/core/grappler/optimizers/meta_optimizer.cc:202] ...[DEBUG] in OptimizeGraph(), input name:input, shape=[64,224,224,3]
tensorflow/core/grappler/optimizers/meta_optimizer.cc:202] ...[DEBUG] in OptimizeGraph(), input name:label, shape=[64]

So, you may think there is no big deal with that. But, if you take a look at Grappler's Cost Analysis or GetPeakMemoryUsage, you will find if the feed shape is with a specific value for the batch size, all the cost calculation, and memory analysis will be reasonable and acceptable.
For instance, the peak memory usage of ResNet-50 model will be the following result:
Case 1:

peak_mem_usage:425138936  ==> 0.395G

Case 2:

peak_mem_usage:6979111176 ==> 6.5GB

So, what is the consequence?
Ans: For instance, "SwappingPass" in memory_optimizer.cc will not work properly. 

P.S:
Here is an article mentioned about "Static input Batch size"
How to train Keras model x20 times faster with TPU for free
https://www.dlology.com/blog/how-to-train-keras-model-x20-times-faster-with-tpu-for-free/
"Input pipelines running on CPU and GPU are mostly free from the static shape requirement, while in the XLA/TPU environment, static shapes and batch size is imposed."

It also provides a full example:
https://colab.research.google.com/drive/1QZf1WeX3EQqBLeFeT4utFKBqq-ogG1FN