BUG: Inconsistent behaviour between excel engines when writing multiple times using the same ExcelWriter
- [x] I have checked that this issue has not already been reported.

- [x] I have confirmed this bug exists on the latest version of pandas.

- [x] (optional) I have confirmed this bug exists on the master branch of pandas.

---

#### Code Sample, a copy-pastable example

```python
import pandas as pd
import io

df = pd.DataFrame({"A": [0, 1], "B": [10, 11]})

for engine in ["openpyxl", "xlsxwriter", "odf"]:
    excel = io.BytesIO()
    with pd.ExcelWriter(excel, engine=engine) as writer:
        df.to_excel(writer, sheet_name="foo", columns=["A"], index=False)
        df.to_excel(writer, sheet_name="foo", columns=["B"], startcol=1, index=False)

    result = pd.read_excel(excel, "foo")
    print(engine)
    print(result)
    print()
```

Produces:
```
openpyxl
   A   B
0  0  10
1  1  11

xlsxwriter
   A   B
0  0  10
1  1  11

odf
     A Unnamed: 1
0  0.0        NaN
1  1.0        NaN
2  NaN          B
3  NaN         10
4  NaN         11
```

Adding this test to `test_writers.py` (line 1327) will also catch the issue:
```python

    def test_excel_multiple_writes_one_writer(self, path):
        df = DataFrame({"A": [0, 1], "B": [10, 11]})

        with ExcelWriter(path) as writer:
            df.to_excel(writer, columns=["A"], index=False)
            df.to_excel(writer, columns=["B"], startcol=1, index=False)

        result = pd.read_excel(path)
        tm.assert_frame_equal(result, df)
```

#### Problem description
This came up when implementing #40231, the behaviour between the engines here seems to be inconsistent.

#### Output of ``pd.show_versions()``

<details>

INSTALLED VERSIONS
------------------
commit           : 6baec67643923ae93b685bdec01105b51f1c0a94
python           : 3.7.3.final.0
python-bits      : 64
OS               : Windows
OS-release       : 10
Version          : 10.0.19041
machine          : AMD64
processor        : Intel64 Family 6 Model 60 Stepping 3, GenuineIntel
byteorder        : little
LC_ALL           : None
LANG             : en_US.UTF-8
LOCALE           : None.None

pandas           : 1.3.0.dev0+979.g6baec67643.dirty
numpy            : 1.20.0
pytz             : 2019.1
dateutil         : 2.8.1
pip              : 20.3.3
setuptools       : 41.4.0
Cython           : 0.29.21
pytest           : 6.2.2
hypothesis       : 6.1.1
sphinx           : 2.4.0
blosc            : None
feather          : 0.4.0
xlsxwriter       : 1.3.7
lxml.etree       : 4.4.1
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : 2.10.1
IPython          : 7.5.0
pandas_datareader: None
bs4              : 4.8.0
bottleneck       : None
fsspec           : None
fastparquet      : None
gcsfs            : None
matplotlib       : 3.1.0
numexpr          : 2.7.1
odfpy            : None
openpyxl         : 3.0.6
pandas_gbq       : None
pyarrow          : 0.13.0
pyxlsb           : None
s3fs             : None
scipy            : 1.3.0
sqlalchemy       : 1.3.13
tables           : 3.6.1
tabulate         : None
xarray           : None
xlrd             : 2.0.1
xlwt             : 1.3.0
numba            : None

</details>
