You allude to this in your comment, so I'll add an example of how I've addressed this by manipulating linewidth rather than alpha to get a similar visualization of distribution that still has sharp lines.

Here's a replication of your current approach:

import matplotlib.pyplot as plt
import numpy as np
num_lines = 1000
np.random.seed(42)
xs = np.linspace(0, 10, 100).reshape(1,-1)
ys = xs*np.random.normal(1,1,(num_lines,1)) + np.random.normal(0, 1, (num_lines,100))
for y in ys:
    l = plt.plot(xs.flatten(), y, 'k', alpha=0.01)
    l[0].set_rasterized(False)
plt.savefig('ex.svg')
plt.show()

Here's an alternative -- I also try to explicitly tell matplotlib not to rasterize via ax.set_rasterization_zorder(None) (I believe this is the same as your l[0].set_rasterized(False) call).

The difference is that I switch to manipulating linewidth rather than alpha. I think the effect is fairly similar.

fig, ax = plt.subplots()
ax.set_rasterization_zorder(None)

num_lines = 1000
np.random.seed(42)
xs = np.linspace(0, 10, 100).reshape(1, -1)
ys = xs * np.random.normal(1, 1, (num_lines, 1)) + np.random.normal(0, 1, (num_lines, 100))
for y in ys:
    ax.plot(xs.flatten(), y, color='black', linewidth=0.01)
fig.savefig('ex_width.svg', format='svg')

When you zoom way in, you can see that the alpha approach (left) is fuzzier than the linewidth approach (right):