to_string() not easily reversible for multi-index DataFrames
#### Code Sample, a copy-pastable example if possible

```python
import pandas
import numpy as np
from itertools import product
df1 = pandas.DataFrame(product(['a', 'b'], range(3)), columns=['idx1', 'idx2'])
df2 = pandas.DataFrame(np.random.rand(6, 2), columns=['col1', 'col2'])
df  = pandas.concat([df1, df2], axis=1)
df.set_index(['idx1','idx2'], inplace=True)
with open('test.dat', 'w') as file:
    file.write(df.to_string())   
df_read = pandas.read_csv('test.dat')
print(df.values)
print(df_read.values)
df.equals(df_read)  # -> False
```
#### Problem description

I wanted to save a pandas DataFrame in human readable form, that is, as a text file with nice vertical alignment. The `to_string` function achieves precisely this, whereas `to_csv` does not.

I have saved data like this before, and it works just fine when one does not save the index. In this case it can be loaded via `pandas.read_csv(file, sep=r'\s+')`. I tried  using the `index_cols` and `header` parameters but nothing seems to work properly.

I also made a [StackExchange thread](https://stackoverflow.com/questions/55023981/pands-read-multi-index-dataframe-reverse-to-string).


#### Expected Output
```python
True
```
#### Output of ``pd.show_versions()``

<details>

INSTALLED VERSIONS
------------------
commit: None
python: 3.6.8.final.0
python-bits: 64
OS: Linux
OS-release: 4.18.0-15-generic
machine: x86_64
processor: x86_64
byteorder: little
LC_ALL: None
LANG: en_US.UTF-8
LOCALE: en_US.UTF-8

pandas: 0.24.1
pytest: None
pip: 19.0.3
setuptools: 40.8.0
Cython: None
numpy: 1.16.2
scipy: 1.2.1
pyarrow: None
xarray: None
IPython: 7.3.0
sphinx: 1.8.4
patsy: 0.5.1
dateutil: 2.8.0
pytz: 2018.9
blosc: None
bottleneck: None
tables: None
numexpr: None
feather: None
matplotlib: 3.0.2
openpyxl: None
xlrd: None
xlwt: None
xlsxwriter: None
lxml.etree: None
bs4: None
html5lib: None
sqlalchemy: None
pymysql: None
psycopg2: None
jinja2: 2.10
s3fs: None
fastparquet: None
pandas_gbq: None
pandas_datareader: None
gcsfs: None

</details>
