The number of photos you can see on your device is limited to the amount of space you have available for them to be loaded. Do you have "Optimize Photos" turned on in Settings>Photos under iCloud Photo Library? If not, you want to set it to Optimize, because clearly, there is not enough space on your device to house all 2000 photos in full resolution.
iCloud Photo Library will dynamically change the number of photos on your device to correspond with the amount of available memory you have to do so:

iCloud Photo Library keeps all of your photos and videos in their original, high-resolution version. You can save space on your device when you turn on Optimize Storage.
On your iPhone, iPad, or iPod touch:
- Go to Settings.
- Tap iCloud > Photos.
- Choose Optimize [device] Storage.
On your Mac:
- Open the Photos app and click Photos in the menu bar.
- Click Preferences.
- Go to the iCloud tab and choose a storage setting.

If you turn on Optimize Storage, iCloud Photo Library automatically manages the size of your library on your device. Your original photos and videos are stored in iCloud and space-saving versions are kept on your device. Your library is optimized only when you need space, starting with the photos and videos you access least. You can download the original photos and videos over Wi-Fi or cellular when you need them. You can use Optimize Storage on your iPhone, iPad, iPod touch, and Mac.
Here is a link to both iCloud Photo Library help articles from Apple:

iCloud Photo Library keeps all of your photos and videos in their original, high-resolution version. You can save space on your device when you turn on Optimize Storage.
On your iPhone, iPad, or iPod touch:
- Go to Settings.
- Tap iCloud > Photos.
- Choose Optimize [device] Storage.
On your Mac:
- Open the Photos app and click Photos in the menu bar.
- Click Preferences.
- Go to the iCloud tab and choose a storage setting.

If you turn on Optimize Storage, iCloud Photo Library automatically manages the size of your library on your device. Your original photos and videos are stored in iCloud and space-saving versions are kept on your device. Your library is optimized only when you need space, starting with the photos and videos you access least. You can download the original photos and videos over Wi-Fi or cellular when you need them. You can use Optimize Storage on your iPhone, iPad, iPod touch, and Mac.
Here are two Apple Support articles that may help:
iCloud Photo Library FAQ - Apple Support
iCloud Photo Library Help - Apple Support
Cheers,
GB