PERF: cache indexers

[jbrockmendel]

Resolves #4702

and avoid _default_to_pandas in a few places.

• [x] commit message follows format outlined here
• [x] passes flake8 modin/ asv_bench/benchmarks scripts/doc_checker.py
• [x] passes black --check modin/ asv_bench/benchmarks scripts/doc_checker.py
• [x] signed commit with git commit -s
• [x] Resolves #4702
• [ ] tests added and passing
• [ ] module layout described at docs/development/architecture.rst is up-to-date
• [ ] added (Issue Number: PR title (PR Number)) and github username to release notes for next major release

[mvashishtha]

@jbrockmendel thank you for making this PR. Could you please make it conform to the contributing guidelines by doing the following:

• File an issue with a short description of the benefits of caching indexers.
• Follow the commit message format here. The Modin CI will fail if you don't do this.
• Link to the issue in the PR description with "Resolves #{issue_number}"

Is the default_to_pandas change unrelated to the cached_property change? If so, I think the changes should get separate issues and PRs, even though each one is very small.

[jbrockmendel]

Is the default_to_pandas change unrelated to the cached_property change? If so, I think the changes should get separate issues and PRs, even though each one is very small.

sure.

[codecov[bot]]

Codecov Report

Merging #4701 (61230fe) into master (c67324b) will decrease coverage by 3.03%. The diff coverage is 100.00%.

:exclamation: Current head 61230fe differs from pull request most recent head 88337d5. Consider uploading reports for the commit 88337d5 to get more accurate results

@@            Coverage Diff             @@
##           master    #4701      +/-   ##
==========================================
- Coverage   69.95%   66.92%   -3.04%     
==========================================
  Files         265      265              
  Lines       19638    19636       -2     
==========================================
- Hits        13738    13141     -597     
- Misses       5900     6495     +595     

Impacted Files	Coverage Δ
modin/pandas/base.py	80.81% <100.00%> (-14.32%)	:arrow_down:
modin/experimental/sklearn/__init__.py	0.00% <0.00%> (-100.00%)	:arrow_down:
modin/experimental/xgboost/__init__.py	0.00% <0.00%> (-100.00%)	:arrow_down:
modin/experimental/xgboost/test/__init__.py	0.00% <0.00%> (-100.00%)	:arrow_down:
modin/experimental/xgboost/test/test_default.py	0.00% <0.00%> (-100.00%)	:arrow_down:
modin/experimental/xgboost/test/test_dmatrix.py	0.00% <0.00%> (-100.00%)	:arrow_down:
modin/experimental/xgboost/test/test_xgboost.py	0.00% <0.00%> (-100.00%)	:arrow_down:
modin/experimental/core/execution/ray/__init__.py	0.00% <0.00%> (-100.00%)	:arrow_down:
...n/experimental/sklearn/model_selection/__init__.py	0.00% <0.00%> (-100.00%)	:arrow_down:
...mental/sklearn/model_selection/train_test_split.py	0.00% <0.00%> (-100.00%)	:arrow_down:
... and 124 more

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[YarShev]

@jbrockmendel, take a look at CI jobs. Some of them failed. Please also format the PR to follow the convention (PR title, commit message, release note, etc.).